Find the coordinates of a point on a circle with radius 30 corresponding to an angle of 15 ∘

Question

Find the coordinates of a point on a circle with radius 30 corresponding to an angle of 

(x,y) = ( , )

please explain as simple as possible

Answer 1

y=rsin15 = 30(.2558) = 7.76

x=rcos15 =30(.966) = 28.98

(x,y) = (29,7.8) in rectangular coordinates =(r, theta)= (30, pi/12) in polar coordinates. pi/12 = 15 degrees

r^2 = x^2 +y^2

1 = cos^2(theta) + sin^2(theta)

r^2 = r^2cos^2(theta) + r^2sin^2(theta)

=x^2 + y^2

x=rcos(theta)

y=rsin(theta)

use a calculator to find sin15 and cos15

or use half angle formulas with sin30= 1/2 and cos30=(1/2)sqr3

Answer 2

(x,y) = (30cos15°, 30sin15°)