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

Answer 1

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.