Suppose an angle has a measure of a radians swept counterclo

Suppose an angle has a measure of a radians (swept counter-clockwise from the 3 o\'clock position) on a circle with a radius of r inches. Use the sine and cosine function to express the coordinates of the terminal point (x, y) in radius lengths and inches. a. The coordinates of the terminal point (measured in radius lengths). (x, y) = b. The coordinates of the terminal point (measured in inches).

Solution

The equation of a circle with origin as center and radius r , in polar coordinates is

x= r cos(theta)

y= r sin(theta)

Where theta is angle with positive x axis.

Therefore coordinates of given point on circle is

x = r cos(a)

y= r sin(a)

The sign will be taken care by angle a.

Here, angle \"theta\" = a radians