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Problem 12

Radians to Degrees In Exercises 11 and $12$ convert the radian measure to degree measure.

(a) $\frac{7 \pi}{3} \quad$ (b) $-\frac{11 \pi}{30}$ (c) $\frac{11 \pi}{6} \quad$ (d) 0.438

Answer

(a) $420^{\circ}$

(b) $-66^{\circ}$

(c) $330^{\circ}$

(d) 25$\cdot 11^{0}$

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## Discussion

## Video Transcript

12 asks us to convert the following rating measures. Now we'll start with a and the one thing we want to remember while converting radiant measures to degree members is that we have a special conversion factor. And that is we will multiply our radiant measures times 360 degrees over to pie. And that equals degrees. So just burn that into your mind when you're doing these conversions. All right, so for heart A, we do seven pi over three times 3 60 over to pie. And this is where you're just gonna have to do a lot of algebra. Oops. So, you know, the pies are gonna cancel out. You're gonna be left with seven times 3 60 over three times to which is six. We know that 360 divided by six is going to equal 120. So the answer is going to be Oh, not 1 20 It's gonna be 60 actually, because that's what it is. And then seven times 60 is 420 so the answer is going to be 420 degrees moving on to part B. We're gonna do the exact same process. Just gonna have different numbers It's a negative. 11 pie over 30 times, 360 degrees divided by two pi. How's he gonna cancel out? We get negative 11 times 360 degrees over 30 times, too, which is 60. This is pretty nice because 360 divided by 60 equal six. So negative 11 times six equals Negative. 66 degrees moving on the part. See? Halfway done. We have 11 pi over six. We're gonna multiply. I you guessed it 360 degrees. That's a zero over to pie pies. Cancel out. We get 11 times 360 degrees over 12. Now this Let me think about it for just a second. This is gonna be the same as 62. Yes. Oh Oh 360. Vetted by 12 was gonna equal 30. So we have 11 times 30 degrees. That's gonna be 330 degrees. All right. And then for the last one, heart D we have 0.438 now for this one. Um, you don't have to express it in a fraction. We can just go ahead and use our calculator. What were you gonna do in your calculators? You're gonna input this conversion factor. Multiply 0.4338 times 3 60 divided by two and you're going to get to the answer is 25 0.0 96 degrees. We used our calculator for that one. All right, and there you have it. Those four radiance have been converted into degrees.

## Recommended Questions

Radians to Degrees In Exercises 11 and $12,$ convert the radian measure to degree measure.

$\begin{array}{lll}{\text { (a) } \frac{3 \pi}{2}} & {\text { (b) } \frac{7 \pi}{6}} & {\text { (c) }-\frac{7 \pi}{12}}\end{array} \quad$ (d) $-2.367$

In Exercises $21-28,$ convert each angle in radians to degrees.

$$

\frac{11 $$\frac{11 \pi}{6}=330^{\circ}$$\pi}{6}

$$

Convert the radian measures to degrees.

A. $5 \pi / 6$

B. $11 \pi / 6$

C. 0

Convert the given radians measure to degrees.

(a) $\frac{3 \pi}{5} \quad$ (b) $\frac{\pi}{7}$

(c) $2 \quad$ (d) 3

In Exercises $21-28,$ convert each angle in radians to degrees.

$$

\frac{11 \pi}{6}

$$

In Exercises $3-6,$ determine the quadrant in which each angle lies. (The angle measure is given in radians.)

$$

\text { (a) } \frac{7 \pi}{4} \quad \text { (b) } \frac{11 \pi}{4}

$$

Convert the radian measures to degrees.

A. $\pi / 12$

B. $\pi / 6$

C. $\pi / 4$

In Exercises $11-14$ , determine two coterminal angles in radian measure (one positive and one negative) for each angle. (There are many correct answers).

$$

\text { (a) }-\frac{9 \pi}{4} \quad \text { (b) }-\frac{2 \pi}{15}

$$

In Exercises 17-22, determine the quadrant in which each angle lies. (The angle measure is given in radians.)

(a) $-\frac{5\pi}{6}$

(b) $-\frac{11\pi}{9}$

Convert the given radians measure to degrees.

(a) $\frac{\pi}{4} \quad$ (b) $\frac{\pi}{3}$

(c) $\frac{\pi}{6} \quad$ (d) $\frac{4 \pi}{3}$