Question

find the coordinates of a point on a circle with radius 30 corresponding to an angle of 55°

(x,y) = ( , )

round your answers to three decimal places.

question help: video

Explanation:

Step1: Calculate the x - coordinate

Use the formula \(x = r\cos\theta\). Here \(r = 30\) and \(\theta=55^{\circ}\).
\(x = 30\cos(55^{\circ})\)
Since \(\cos(55^{\circ})\approx0.5736\), then \(x = 30\times0.5736 = 17.208\)

Step2: Calculate the y - coordinate

Use the formula \(y = r\sin\theta\). Here \(r = 30\) and \(\theta = 55^{\circ}\).
\(y=30\sin(55^{\circ})\)
Since \(\sin(55^{\circ})\approx0.8192\), then \(y = 30\times0.8192=24.576\)

Answer:

\((17.208,24.576)\)