Question

use reference angles to find the exact value of the following expression. do not use a calculator. tan 765°. determine the reference angle for 765°. the reference angle is □°.

Explanation:

Step1: Find coterminal angle

Subtract multiples of 360° from 765°. $765 - 2\times360=765 - 720 = 45^{\circ}$.

Step2: Determine reference angle

Since 45° is in the first - quadrant, the reference angle of 45° is 45°.

Step3: Find tangent value

We know that $\tan45^{\circ}=1$.

Answer:

The reference angle is 45°. The value of $\tan765^{\circ}=1$.