### Home > APCALC > Chapter 1 > Lesson 1.4.2 > Problem1-158

1-158.

Without using a calculator, determine the exact value of each of the following trig expressions.

1. $\sin(\frac { 5 \pi } { 6 })$

Visualize the angle on the unit circle. What side ratio correspond with that angle? What quadrant is it in? (This will determine whether your answer will be positive or negative.)

$\frac{1}{2}$

1. $\cos(\frac { - 3 \pi } { 4 })$

See hint in part (a).

1. $\tan(\frac { \pi } { 3 })$

$\tan(a)=\frac{\text{sin}(a)}{\text{cos}(a)}$

1. $\sec(\frac { 5 \pi } { 3 })$

$\sec(a)=\frac{1}{\text{cos}(a)}$