How to solve parametric equations with sin and cos

How to solve parametric equations with sin and cos. Boys lap 1. Applications of Parametric Equations. Basic geometry* will give us the equations: x(θ) = a[θ − sin(θ)] y(θ) = a[1 −cos(θ)] *The x coordinate is given by the difference between the arclenght aθ, wich is Example 3: Graphing Parametric Equations and Rectangular Form Together. Now, if we transform our parametric equations, x (t) and y (t), to y (x), consider this: The car is running to the right in the direction of an increasing x-value on the graph. y = 3x2−ln(4x +2) y = 3 x 2 − ln. x = r cos (t) y = r sin (t) Dec 27, 2019 · So i'm struggling with these parametric equations in Sympy. Dec 11, 2022 · The curve sketched out in Example 11. Compare the two graphs. Calculus. Sometimes equations are simpler to graph when written in rectangular form. t is the parameter, which ranges from 0 to 2π radians. Take the inverse secant of both sides of the equation to extract t t from inside the secant. 5) = π/6. Then dy dt = dy dx ⋅ dx dt by the Chain Rule. (c) Set up, but do not evaluate, a double integral for the surface area of the surface in part Nov 16, 2022 · Let’s just jump into the examples and see how to solve trig equations. sin((2pi/365)t) = 22/52 = . Solve for the angle. x t. plane-curves. But he might as well have drawn the car running over the side of a cliff leftwards in the Free math problem solver answers your trigonometry homework questions with step-by-step explanations. The complete solution is the result of both the positive and negative portions of the solution. 1: Graph of the line segment described by the given parametric equations. sec x = 1. sin x. display import display sp. Find a function y = f(x) whose graph gives the parametric equations. Rewrite the equation as sec(t) = x sec ( t) = x. This answer has not been graded yet. I can't find anything here about ambiguous triangles. 2 Find the area under a parametric curve. Nov 16, 2022 · Back to Problem List. We have already seen how to compute slopes of curves given by parametric equations—it is how we computed slopes in polar coordinates. Girls lap 1. A range of t t ’s for a single trace of the parametric curve. I'm working on this particular question and I went with the double angle identity of cos, so cos(2theta)=cos(theta)*cos(theta)-sin(theta)*sin(theta) which is simply cos^2(theta)-sin^2(theta). Calculus questions and answers. Sorted by: 7. 5. In this unit, you'll explore the power and beauty of trigonometric equations and identities, which allow you to express and relate different aspects of triangles, circles, and waves. Calculate the derivative \(\dfrac{dy}{dx}\) for each of the following parametrically defined plane curves, and locate any critical points on their respective graphs. Show All Steps Hide All Steps. 44, 44. Answer. 6 based on 20924 reviews. x(t) = (a − b)cost + bcos(a − b b)t. Jul 13, 2022 · This suggests that for each value of \(t\), these parametric equations give a point on a circle of ra dius 3 at the angle corresponding to \(t\). Many of the advantages of parametric equations become obvious when applied to solving real-world problems. y(t) = (a − b)sint − bsin(a − b b)t. Sep 7, 2022 · The graph of this curve appears in Figure 11. 3 Use the equation for arc length of a parametric curve. Expert-verified. The parametric equations are simple linear expressions, but we need to view this problem in a step-by-step fashion. xc,yc is circle's center point. Graph lines, curves, and relations with ease. x=x(t)andy=y(t) x = x ( t) and y = y ( t) are called parametric equations and t t is called the parameter. I'm trying to solve a system of equations. 4 Apply the formula for surface area to a volume generated by a parametric curve. So in general we can say that a circle centered at the origin, with radius r, is the locus of all points that satisfy the equations. Then, we plug this into the second equation given for y, which gives us Sep 1, 2020 · Answer. Then graph the rectangular form of the equation. and of. (c) The new setup, now that the ant has moved closer to the center of the wheel. From the above we can find the coordinates of any point on the circle if we know the radius and the subtended angle. 5 Calculus with Parametric Equations. Step 3. tan x sin x. First, construct the graph using data points generated from the parametric form. (89. If we superimpose coordinate axes over this graph, then we can assign ordered pairs to each point on the ellipse (). x = a cos ty = b sin t. The parametric equation of a circle. y=2sin_t_. (b) Use the parametric equations in part (a) to graph the surface for the case a = 2, b = 5, c = 4. The coordinates are measured in meters. Differentiating Parametric Equations. Construct a table of values like that in Table \(\PageIndex{3}\). Example 10. ⭐️ Rating. This is called a curtate cycloid. Now, in a calculus class this is not a typical trig equation that we’ll be asked to solve. Tap for more steps Multiply both sides of the equation by 2 2. Sep 27, 2023 · September 27, 2023 by GEGCalculators. There are a number of shapes that cannot be represented in the form. x2 3 +y2 3 =cos2 θ sine of an angle is the y value of the radius when it is at that angle, so it is even less than sin(pi/6), so we know that at least. They help us find the path, direction, and position of an object at any given time. Rewrite the equation as cos(t) = x cos ( t) = x. Limits on x x and y y. In this case, [latex]y\left (t\right) [/latex] can be any expression. Sep 1, 2020 · An object travels at a steady rate along a straight path \((−5, 3)\) to \((3, −1)\) in the same plane in four seconds. 1 Find the slope of the cycloid x = t − sin t x = t − sin t, y = 1 − cos t y = 1 − cos t . cos( ) sin( ) x hr t Oct 31, 2012 · x = (R + a · sin (n·θ)) · cos (θ) + xc. Graph the parametric equations [latex]x=5\cos t [/latex] and [latex]y=2\sin t [/latex]. In this video, we learn about parametric equations using the example of a car driving off a cliff. Take the inverse cosine of both sides of the equation to extract t t from inside the cosine. (2) Let’s start with the parametrized curves. You'll learn how to use trigonometric functions, their inverses, and various identities to solve and check equations and inequalities, and to First step is to rearrange equation into A=sin(B) form, note how you still have the same x-solutions Nov 27, 2012 · 1 Answer. Just plug in the parametric expressions for x x and y y and you have parametric expressions for u u and v v. \) given to describe this curve are a system of equations, we can use the technique of substitution as described in Section 8. The equation for x gives horizontal distance, and the equation for y gives the vertical distance. Any tangent line must have the same slope as dy/dx (which are now constants), and as well must pass through r evaluated at the Nov 16, 2022 · For problems 12 – 14 write down a set of parametric equations for the given equation that meets the given extra conditions (if any). 6 Converting from rectangular to parametric Find a parameterization for the hyperbola ( x - 2 ) 2 9 - ( y - 3 ) 2 4 = 1 . The point labeled F 2 F 2 is one of the foci of the ellipse; the other focus is occupied by the Sun. Find parametric equations for the position of the object. See (Figure), (Figure), and (Figure). However, if we were to graph each equation on its own, each one would pass the vertical line test and therefore would represent a function. x = a sin(u) cos(v), y = b sin(u) sin(v), z = c cos(u), 0 ≤ u ≤ π, 0 ≤ v ≤ 2π. Interestingly, these similar Apr 27, 2023 · Sketch the graph of the parametric equations \(x=2 \cos \theta\) and \(y=4 \sin \theta\), along with the rectangular equation on the same grid. Suppose we have a curve which is described by the following two equations: x = acosq (1) y = asinq (2) We can eliminate q by squaring and adding the two equations: x 2 + y 2 = a 2 cos 2 q + a 2 sin 2 q = a 2. 2. In this section we will find a formula for determining the area under a parametric curve given by the parametric equations, x = f (t) y = g(t) x = f ( t) y = g ( t) We will also need to further add in the assumption that the curve is traced out exactly once as t t increases from α α to β β. I end up with sine and cosine in one equation and the parameter of both as the last unknown. x = 3sin(t) y =−4cos(t) 0 ≤ t ≤ 2π x = 3 sin ( t) y = − 4 cos ( t) 0 ≤ t ≤ 2 π. But then how do I relate that to the x=sin(theta)? Feb 12, 2022 · Eliminate the parameter from the given pair of parametric equations and write as a Cartesian equation: \(x(t)=2 \cos t\) and \(y(t)=3 \sin t\). (b) The ant’s path of motion after he climbs closer to the center of the wheel. x = 5cos(θ) x = 5 cos ( θ) Replace t t in the equation for y y to get the equation in terms of x x. Step 4. Eliminate the Parameter x=5cos (theta) , y=6sin (theta) x = 5cos (θ) x = 5 cos ( θ) , y = 6sin(θ) y = 6 sin ( θ) Set up the parametric equation for x(t) x ( t) to solve the equation for t t. Take the inverse sine of both sides of the equation to extract t t from inside the sine. Trigonometric equations are, as the name implies, equations that involve trigonometric functions. Take the specified root of both sides of the equation to eliminate the exponent on the left side. Let x = 5t2 − 6t + 4 and y = t2 + 6t − 1, and let C be the curve defined by these equations. So it looks like this-. Find the equations of the tangent and normal lines to C at t = 3. cot x = 1 = cos x. If x = t2 − 3 and y = t8, then dx dt = 2t and dy dt = 8t7. However, there are various methods we can use to rewrite a set of parametric equations as a Cartesian equation. Mar 20, 2016 · Method 1 (easy) \begin{align*} x^2 &= \sin^2 \left( \frac{\theta}{2} \right) \text{ and } \\ y^2 &= \cos^2 \left( \frac{\theta}{2} \right) \text{ so } \\ x^2 + y^2 x = (v0cosθ)t y = − 1 2gt2 + (v0sinθ)t + h. cos x. 2 - 2cos²x + cosx - 1 = 0. This equation is very similar to the one used to define a circle, and much of the discussion is omitted here to avoid duplication. Note, sec x is not the same as cos -1 x (sometimes written as arccos x). Subtract from both sides of the equation. What minimum parameter domain is required to draw the entire Set up the parametric equation for x(t) x ( t) to solve the equation for t t. (a) Determine the surface defined by the parametric equations. (2) Solve for pts $(x,y)$ where implicit eqn and gradient simultaneously vanish. Boys lap 3. Last Modified: Nov 29, 2023. Solving Linear Trigonometric Equations in Sine and Cosine. It’s important to remember to use the plus-or-minus sign ± when taking the square root of both sides; otherwise you could overlook some solutions. Girls lap 2. It should be obvious that the entire ellipse is traced, but it is left as an exercise to show what the parameter t represents. 1 for t: x(t) = 2t + 3. For example, for parametric equations x = 2t and y = t^2, we can eliminate t by solving for t in the first equation (t = x/2) and substituting it into the second equation Jun 15, 2021 · The parametrization determines the orientation and as we shall see, different parametrizations can determine different orientations. The first is as functions of the independent variable t. However, when θ = π, the denominator is also 0, so we cannot conclude that the tangent line is horizontal. Parametric equations define x and y as functions of a third parameter, t (time). 𝑓(𝜃) = cos(𝜃) − sin(𝑎𝜃) and 𝑔(𝜃) = sin(𝜃) + cos(𝑎𝜃) with 𝑎 ∈ ℝ∖{0}. We can eliminate the parameter by first solving Equation 11. The set of points (x,y) ( x, y) obtained as t t varies over the interval I I is called the graph of the parametric equations. so, 2 ( sin²x ) = 2 (1 - cos²x) Now we plug that into your challenge problem: 2 (1 - cos²x) + cos x - 1 = 0. See Parametric equation of a circle as an introduction to this topic. and then take square root of both sides: tan ( B /2) = ±√ 1/3 = ±√ 3 /3. In some instances, the concept of breaking up the equation for a circle into two functions is similar to the concept of creating parametric equations, as we use two functions to produce a non-function. " Oct 28, 2020 · To solve it, add 1 to both sides and divide by 3: tan² ( B /2) = 1/3. y =sin3(θ) ⇒ x1 3 = sin θ ⇒ y2 3 =sin2 θ y = sin 3 ( θ) ⇒ x 1 3 = sin θ ⇒ y 2 3 = sin 2 θ. The number of traces of the curve the particle makes if an overall range of t t ’s is provided in the problem. Answer \(\dfrac{x^2}{4}+\dfrac{y^2}{9}=1\) Figure 7. ( 4 x + 2) Solution. Oct 5, 2022 · How do you eliminate the parameter in parametric equations? How do you eliminate the parameter with sin and cos? This video works through three examples of r Calculus. By definition, the system of equations \(\left\{ x = \cos(t), \, y = \sin(t) \right. Eliminate the parameter for the following set of parametric equations, sketch the graph of the parametric curve and give any limits that might exist on x x and y y. 1 certainly looks like a parabola, and the presence of the \(t^{2}\) term in the equation \(x=t^{2}-3\) reinforces this hunch. Step 1. This also means it is in the domain of arcsin, which is good. About this unit. Suppose for the moment that we are able to re-write this as y(t) = f(x(t)) . And you'd implicitly assume, of course, as x increases, t (time) increases. If x x and y y are continuous functions of t t on an interval I I, then the equations. 1: Hyperbolas. Remember, you cannot divide by zero and so these definitions are only valid Nov 29, 2023 · Parametric Equations for Circles and Ellipses. 3. Figure 4. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Graph the parametric equations \(x=5 \cos t\) and \(y=2 \sin t\). a is sinusoid amplitude. Start Solution. Indeed, these equations describe the equation of a circle, drawn counterclockwise. The method used in your second link seems appropriate—the direction vector of the tangent line at any point on $\langle x(t),y(t),z(t)\rangle=\langle\cos t,\sin t,t\rangle$ is $\langle x'(t),y'(t),z'(t)\rangle=\cdots$ (no partial derivatives needed) and you know a point on the line, so you can write a parametric equation for the tangent line. A parametric equation is a set of equations that express a set of quantities as explicit funct Dec 29, 2020 · If the normal line at t = t0 has a slope of 0, the tangent line to C at t = t0 is the line x = f(t0). 7. If the equations contain sine and cosine, or tangent and secant, it might be easier to solve each equation for the trigonometric function and use a Pythagorean Identity such as \(\sin^2 θ + \cos^2 θ = 1\) or \(1 + \tan^2 θ = \sec^2 Nov 16, 2022 · Section 9. Instead of numerical coordinates, use expressions in terms of t, like (cos t, sin t ). Rewrite the equation as . 😍 Step by step. Depending on the units involved in the problem, use g = 32ft/s2 or g = 9. ⁡. x = 4−2t y = 3+6t −4t2 x = 4 − 2 t y = 3 + 6 t − 4 t 2. We Nov 10, 2020 · This video shows how to graph parametric equations involving trigonometric functions and how to eliminate their parameter. 6, and c = 3. When we graph parametric equations, we can observe the individual behaviors of. Since the parametric equations \(\left\{x=t^{2}-3, y=2 t-1\right. . At \(t = 0\), the graph would be at \(x = 3\cos(0), y = 3\sin(0)\), the point (3,0). A rectangular equation, or an equation in rectangular form is an equation composed of variables like x x and y y which can be graphed on a regular Cartesian plane. where. Example \(\PageIndex{1}\): Finding the Derivative of a Parametric Curve. x=3cos_t_. 2() + 2) 2 + 2 1 sin 2 () + 2 () 2 + 2 1. cos²x + sin²x = 1. Whether you’re interested in form, function, or both, you’ll love how Desmos handles parametric equations. x 2 3 + y 2 3 = 1. t = x − 3 2. y = 2 sin t. 1: Tangent and Normal Lines to Curves. Nov 10, 2020 · The graph of parametric equations is called a parametric curve or plane curve, and is denoted by C. 10. An example of projectile motion is It gets rid of the messy 2sin²x that makes your equation such a complicated thing to solve. So calculate those to get a formula for dx/dt and dy/dt. The equation of a circle, centred at the origin, is: x 2 + y 2 = a 2, where a is the radius. sin²x = 1 - cos²x. Oct 14, 2019 · If the parametric equations were x = 3*sin(t), y = 1. Solving for dy dx and assuming dx dt ≠ 0 , dy dx = dy dt dx dt a formula that holds in general. This is the parametric equation for the cycloid: x y = r(t − sin t) = r(1 − cos t) x = r ( t − sin t) y = r ( 1 − cos t) How are these equations found in the first place? geometry. Using the trigonometric identity sin2(θ) +cos2(θ) = 1 sin 2 ( θ) + cos 2 ( θ), you can square both of your equations of x x and y y. Often we will solve a This page covers Parametric equations. Graph the parametric equations x = 5 cos t x = 5 cos t and y = 2 sin t y = 2 sin t. n is number of sinusoids on circle. 72) It is beneficial to see how to find the original function given parametric equations to understand the connection. Simplify the left side. But since the sine function has a period of 2π, we know that there are other angles that have the same sine value, such as x = 5π/6, 13π/6, etc. Solution. Parametric Equations. Aug 29, 2023 · x2 a2 + y2 b2 = a2cos2t a2 + b2sin2t b2 = cos2t + sin2t = 1. (1) Find implicit form from parametric. It is a line segment starting at ( − 1, − 10) and ending at (9, 5). If all of this seems hauntingly familiar, it should. y = 6sin(θ) y = 6 sin ( θ) For example, if we have the equation sin (x) = 0. pyplot as plt import sympy as sp from IPython. 1 Determine derivatives and equations of tangents for parametric curves. Two thirds of a cube in exponent is a square , so comes the Astroid x2 3 +y2 3 = 1. Let x = x(t) and y = y(t) . you can also get a pure cartesian equation (non-parametric) on x/y, but just for half Mar 29, 2017 · Learn how to eliminate the parameter in a parametric equation. x2 +y2 = 36 x 2 + y 2 = 36 and the parametric curve resulting from the parametric equations should be at (6,0) ( 6, 0) when t = 0 t = 0 and the Parameterizing a curve involves translating a rectangular equation in two variables, and into two equations in three variables, x, y, and t. Select the first set of parametric equations, x = a cos (bt), y = c sin (at). Oct 3, 2015 · 2 Answers. In this case, y(t) can be any expression. y = (R + a · sin (n·θ)) · sin (θ) + yc. Step 2. x = cos3(θ) ⇒ x1 3 = cos θ ⇒ x2 3 =cos2 θ x = cos 3 ( θ) ⇒ x 1 3 = cos θ ⇒ x 2 3 = cos 2 θ. Example 1 Solve 2cos(t) =√3 2 cos ( t) = 3 . Questions. 10. 3 10. cosec x = 1. What if a question asks you to solve from a description where two triangles exist? Like "Determine the unknown side and angles in each triangle, if two solutions are possible, give both: In triangle ABC, <C = 31, a = 5. Secant, cosecant and cotangent, almost always written as sec, cosec and cot are trigonometric functions like sin, cos and tan. Let’s begin by solving x = 3t+2 for t. Describe the parametric curve. The graph of the parametric equations is in red and the graph of the rectangular equation is drawn in blue dots on top of the parametric equations. x(t) = t y(t) = t2 −3. 2 depicts Earth’s orbit around the Sun during one year. R is circle's radius. Like this: All you need to put is the two equations and the values of t you want to display. Notice in this definition that x and y are used in two ways. init_printing() %matplotlib inline This is what I have to define them: The blue line for positive \(x\) shows the line that this parametric set of equations traces out: Show that hyperbolic cosine and hyperbolic sine functions form a set of parametric equations that translate into the equation for a hyperbola, \(x^2-y^2 = 1\). Show Solution. Although rectangular equations in x and y give an overall picture of an object's path, they do not reveal the position of an object at a specific time. The parameter adopted will be the angle described by the point intially at the origin, the center of the circle and the point of contact between the circle and the x axis. The simplest method is to set one equation equal to the parameter, such as [latex]x\left (t\right)=t [/latex]. Jul 25, 2020 · Answers (2) x = r (t] (1), y = r (t) (2), dx/dt = d r (t) (1) /dt, dy/dt = d r (t) (2) / dt. Setting the denominator to zero we get. 7. Figure \(\PageIndex{9}\) Aug 17, 2020 · A point on the edge of the green circle traces out the red graph, which is called a hypocycloid. \) parametrizes the Unit Circle, giving it a counter-clockwise orientation. Similar in many ways to solving polynomial equations or rational equations, only specific values of the variable will be solutions, if there are solutions at all. (3) Discard those solutions that correspond to cusps. − sin θ − 2 sin θ cos θ = 0. In depth solution steps. Unlock. cos( ) sin( ). 13: (a) The ant climbs up one of the spokes toward the center of the wheel. Girls lap 3. Graph the parametric equations x = 5 cos t x = 5 cos t and y = 2 sin t. Boys lap 2. First solve the identity for sin²x. 8m/s2. The general parametric equations for a hypocycloid are. 1. x = 3 ( cos θ + θ sin θ) View the full answer. 9. One of the reasons we parameterize a curve is because the parametric equations yield more information: specifically, the direction of the object’s motion over time. (a) Set the equations to x = 3 cos (t), y = 3 sin (t) using the sliders for a, b, c, and d. Jan 23, 2021 · Example \(\PageIndex{1}\): Finding the Derivative of a Parametric Curve. Figure 10. 4. Figure 11. Improve your math skills. In x, y x, y coordinates, counterclockwise rotation by θ θ takes (x, y) ( x, y) to (u, v) = (x cos(θ) − y sin(θ), x sin(θ) + y cos(θ)) ( u, v) = ( x cos ( θ) − y sin ( θ), x sin ( θ) + y cos ( θ)). Set up the parametric equation for to solve the equation for . where g accounts for the effects of gravity and h is the initial height of the object. In many calculus books I have, the cycloid, in parametric form, is used in examples to find arc length of parametric equations. A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x, y I'm trying to find the cartesian equation of the curve which is defined parametrically by: $$ x = 2\sin\theta, y = \cos^2\theta $$ Both approaches I take result in the same answer: $$ y = 1 - \s Sep 4, 2020 · Given a parametric curve where our function is defined by two equations, one for x and one for y, and both of them in terms of a parameter t, like x=f(t) and y=g(t), we can eliminate the parameter value in a few different ways. 5 days ago · Graphing parametric equations on the Desmos Graphing Calculator is as easy as plotting an ordered pair. Step 5 Replace in the equation for to get the equation in terms of . Rewrite the equation as sin2(t) = x sin 2 ( t) = x. Rewriting this set of parametric equations is a matter of substituting x for t. 6. For example if you only want to graph the part of the ellipse in Sal's example at the beginning of the video, you put the equations and the values of t . Replace t t in the equation for y y to get the equation in terms of x x. Which you can then substitute into the identity I just stated. Created by Sal Khan. Feb 19, 2024 · Graphing Parametric Equations and Rectangular Form Together. The only difference between the circle and the ellipse is that in The simplest method is to set one equation equal to the parameter, such as x(t) = t. Type in any integral to get the solution, steps and graph. Aug 22, 2020 · With trigonometric parametric equations, you need to be thinking of trigonometric identities. 1. sin θ(1 + 2 cos θ) = 0, so either sin θ = 0 or cos θ = −1/2. 5, we can use the inverse sine function to find one solution: x = sin^-1 (0. y t that defines a circle of radius 1 centered at the origin and multiply both the x- and y-coordinate by a factor of r and add constants h and k to the x- and y-coordinates, respectively, we obtain the system . For example y = 4x + 3 y = 4 x + 3 is a rectangular equation. As t varies over the interval I, the functions x(t) and y(t) generate a set of ordered pairs (x, y). 3 : Area with Parametric Equations. Example 7. x − 3 = 2t. For example, consider the following pair of equations. for all t, then the points (x, y) = (acost, bsint) lie on the ellipse x2 a2 + y2 b2 = 1. Example 2 Solve 2cos(t) =√3 2 cos ( t) = 3 on [−2π,2π] [ − 2 π, 2 π] . Then evaluate at the given time t = 2 to get dx and dy as constants. To find all solutions, we use the general solution: x = π/6 Graph the parametric equations \(x=5 \cos t\) and \(y=2 \sin t\). Rewrite the equation as sin(1 2t) = x sin ( 1 2 t) = x. We compute x′ = 1 − cos t x ′ = 1 − cos t, y Oct 28, 2020 · To solve it, add 1 to both sides and divide by 3: tan² ( B /2) = 1/3. To do this, solve one of the parametric equations for t and substitute the expression into the other equation. Set up the parametric equation for x(t) x ( t) to solve the equation for t t. Oct 14, 2013 · Can be done as follows. To convert parametric equations to rectangular form, express x and y in terms of a parameter (typically denoted as t), then eliminate t. Take the inverse cosine of both sides of the equation to extract from inside the cosine. Example 9. The first is true when θ is 0 or π, the second when θ is 2π/3 or 4π/3. 3: Graphing Parametric Equations and Rectangular Form Together. 7 to eliminate the parameter \(t\) and Nov 16, 2022 · A sketch of the parametric curve (including direction of motion) based on the equation you get by eliminating the parameter. As we observed in the previous chapter, if we start with the system of parametric equations . import matplotlib. Often, more information is obtained from a set of parametric equations. 9: Graph of the hypocycloid described by the parametric equations shown. 5*cos(t) I know I would solve it the following Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Solving these equations for x and y we set x =-3 ⁢ cos ⁡ t + 2 and y = 2 ⁢ sin ⁡ t-3 for 0 ≤ t ≤ 2 ⁢ π. θ is the parameter (angle), from 0 to 2π. 42307 inverse sine or arcsin of both sides 2pi/365 t = arcsin(22/52) divide both sides by 2pi/365 t = arcsin(22/52)365/(2pi) Solving Linear Trigonometric Equations in Sine and Cosine. A more typical example is the next one. Given that the parametric curve. Remove parentheses. ay yh cv ee lg lh po xn tb rl