# 8.04 a graph each pair of parametric equations. (2 points each) x = 3 sin3t y = 3 cos3t a coordinate graph is shown with the x axis

Hey! Hope this helps… ~~~~~~~~~~~~~~~~~~~~ Sorry kept of freezing on me… Solving this is pretty simple, we plug in what t equals in both equations based upon our lovely given notice -4 ≤ t ≤ 4… (My work will be attached below) Now we will have to plot all the points we gathered onto our graph… (The Graph will be attached below) And there you are!

For example,x = 2tx = 2(2) = 4x = 2(3) = 6 Now, you know there are points at (2, 4) and (3, 6). 2. This one is a little tricky, but all it’s saying is that it has a specified domain. The parametric equation only works for values -2 ≤ t ≤ 3. So, you can do the exact same thing, except your line will only exist for points through the x-values -2 and 3. Let’s plug in numbers: y = t + 5y = -2 + 5 = 3y = 1 + 5 = 6 Now you know that this line runs through (-2, 3) and (1, 6). Remember, your line starts at -2 and ends at 3. It can’t go any further than that.

We are given a parametric equation as:             and       Hence, we can represent our equation as: As we know that: Hence, on putting the value in the formula we get the equation in rectangular coordinates as: Hence, this is a equation of a  ASTROID.

The details will depend on your calculator. Attached is a graph using the Desmos calculator.

The following parametric equation graph is shown in the picture in the attachment x = 3 sin (3t) y = 3 cos (3t) Further explanation Firstly , let us learn about trigonometry in mathematics. Suppose the ΔABC is a right triangle and ∠A is 90°. sin ∠A = opposite / hypotenusecos ∠A = adjacent / hypotenusetan ∠A = opposite / adjacent There are several trigonometric identities that need to be recalled, i.e. Let us now tackle the problem! Given : By using the following trigonometric identity, we can combine the two equations above to become : In cartesian coordinates, the above equation will form a circle that has a center at (0,0) and a radius of 3. Learn moreCalculate Angle in Triangle : Periodic Functions and Trigonometry : Trigonometry Formula : Answer details Grade: College Subject: Mathematics Chapter: Trigonometry Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse