A circle centered at 0 0 with radius r has equation x2 y2

A circle centered at (0, 0) with radius r has equation x^2 + y^2 = r^2. (a) Determine the value of b for the point (2, b) which lies on the circle in quadrant I, if the line segment joining (0, 0) and (2, b) forms a 40 degree angle with the x-axis. Round to one decimal. (b) Determine the radius of the circle. Round to one decimal. (c) Determine the length s of the are joining the points (r, 0) and (2, b), for the r and b values you found above.

Solution

a. Tan40 = b/2

That implies b = 2tan40

b. cos40 = 2/r

That implies r = 2/cos40 ,

c.length = r* theta

That implies s = (2/cos40)*(40pi/180)

Here 40pi/180 is nothing but 40 degrees in radians