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9-91.

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

Hint:

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

$\frac { 7 \pi } { 6 }$ radians to degrees.
Hint (a):
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.
Answer (a):
$210^\circ$

$\frac { 5 \pi } { 3 }$ radians to degrees
Hint (b):
Use the Hint or Help from problem 9-90.
Step 1 (b):
$\text{Multiply } \frac{5 \pi}{3} \text{ by } \frac{180}{\pi}.$
Step 2 (b):
Simplify by factoring out Giant Ones.

$45$ degrees to radians
Hint (c):
Use the second part of the Help from problem 9-90.
Answer (c):
$\frac{{\pi}}{4}$

$100^\circ$ to radians
Hint (d):
Use the Help from problem 9-90 or try the More Help:
More Help (d):
$\text{Use the proportion } \frac{\pi}{180°} = \frac{r}{100°}.$

$810^\circ$ to radians
Hint (e):
See parts (c) and (d).

$\frac { 7 \pi } { 2 }$ radians to degrees
Hint (f):
See parts (a) and (b).
Answer (f):
$630^\circ$

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