Express the function 120 degree as function of an acute angle? - Answers

Example: Express sin 120⁰ as a function of an acute angle (an angle between 0⁰ and 90⁰).Solution:Each angle θ whose terminal side lies in quadrant II, III, or IV has associated with it an angle called the reference angle, alpha (alpha is formed by the x-axis and the terminal side).Since 120⁰ lies on the second quadrant, then alpha = 180⁰ - 120⁰ = 60⁰.Since sine is positive in the second quadrant, sin 120⁰ = sin 60⁰.Example: Express tan 320⁰ as a function of an acute angle.Solution:Since 320⁰ lies on the fourth quadrant, then alpha = 360⁰ - 320⁰ = 40⁰.Since tangent is negative in the fourth quadrant, tan 320⁰ = -tan 40⁰.