  ### Home > INT3 > Chapter 9 > Lesson 9.1.7 > Problem9-91

9-91.

Convert each of the following angle measures. Give exact answers.

There are multiple ways to approach these problems. Try different strategies to expand your personal toolkit.

1. $\frac { 7 \pi } { 6 }$ radians to degrees.

Use the Hint from
problem 9-90.
Let $π = 180^\circ$ and simplify.
Notice, you do not need a calculator if you divide $180$ by $6$ as your first step.

$210^\circ$

1. $\frac { 5 \pi } { 3 }$ radians to degrees

Use the Hint or Help from problem 9-90.

$\text{Multiply } \frac{5 \pi}{3} \text{ by } \frac{180}{\pi}.$

Simplify by factoring out Giant Ones.

1. $45$ degrees to radians

Use the second part of the Help from problem 9-90.

$\frac{{\pi}}{4}$

1. $100^\circ$ to radians

Use the Help from problem 9-90 or try the More Help:

$\text{Use the proportion } \frac{\pi}{180°} = \frac{r}{100°}.$

1. $810^\circ$ to radians

See parts (c) and (d).

1. $\frac { 7 \pi } { 2 }$ radians to degrees

See parts (a) and (b).

$630^\circ$