Compute the measure of the angle between 0 and 360 degrees s

Compute the measure of the angle between 0 and 360 degrees swept counterclockwise from 3 o\'clock position on the unit circle whose terminal ray intersects the circle at the point with given y-coordinate and in the given quadrant. a. 0.1 in Quadrant I. degrees Preview b, z =-0.5 in Quadrant 11. -1120 degrees Preview c. z =-0.2 in Quadrant lll. =178.465379437061degrees Preview d z-0.9 in Quadrant IV. 1334.1581 degreesPreview

Solution

a) x = 0.1 in quadrant 1

cos theta = 0.1 / 1

theta = cos^-1 (0.1)

theta = 84.2608

c) x = -0.2 in quadrant 3

cos theta = -0.2 / 1

theta = cos^-1 (0.2)

theta = 78.463

theta in quadrant 3 = 180 + 78.463 = 258.463