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 / hypotenuse
cos ∠A = adjacent / hypotenuse
tan ∠A = opposite / adjacent
There are several trigonometric identities that need to be recalled, i.e.
\(cosec ~ A = \frac{1}{sin ~ A}\)
\(sec ~ A = \frac{1}{cos ~ A}\)
\(cot ~ A = \frac{1}{tan ~ A}\)
\(tan ~ A = \frac{sin ~ A}{cos ~ A}\)
Let us now tackle the problem!
Given :
\(x = 3 \sin (3t) \Rightarrow \sin (3t) = \frac{x}{3}\)
\(y = 3 \cos (3t) \Rightarrow \cos (3t) = \frac{y}{3}\)
By using the following trigonometric identity, we can combine the two equations above to become :
\(\sin^2 \theta + \cos^2 \theta = 1\)
\(\sin^2 (3t) + \cos^2 (3t) = 1\)
\((\frac{x}{3})^2 + (\frac{y}{3})^2 = 1\)
\(x^2 + y^2 = 3^2\)
In cartesian coordinates, the above equation will form a circle that has a center at (0,0) and a radius of 3.
Learn more
- Calculate Angle in Triangle : https://brainly.com/question/12438587
- Periodic Functions and Trigonometry : https://brainly.com/question/9718382
- Trigonometry Formula : https://brainly.com/question/12668178
Answer details
Grade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse
