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Trigonometry : Radians and Conversions

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Example Questions

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Example Question #31 : Circles

Convert $2^{\circ}$ into radians.

Possible Answers:

$\frac{\pi}{180}$

$\frac{\pi}{90}$

$\frac{\pi}{360}$

$2\pi$

$\pi$

Correct answer:

$\frac{\pi}{90}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$2*\frac{\pi}{180}=\frac{\pi}{90}$ .

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Example Question #591 : New Sat

Convert $10^{\circ}$ into radians.

Possible Answers:

$\frac{\pi}{180}$

$\frac{\pi}{36}$

$\frac{\pi}{90}$

$\frac{10\pi}{9}$

$\frac{\pi}{18}$

Correct answer:

$\frac{\pi}{18}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$10*\frac{\pi}{180}=\frac{\pi}{18}$ .

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Example Question #34 : Radians

Convert $600^{\circ}$ into radians.

Possible Answers:

$\frac{11\pi}{5}$

$3\pi$

$\frac{\pi}{5}$

$\frac{10\pi}{9}$

$\frac{10\pi}{3}$

Correct answer:

$\frac{10\pi}{3}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$600*\frac{\pi}{180}=\frac{10\pi}{3}$ .

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Example Question #31 : Radians And Conversions

Convert $\frac{\pi}{2}$ into degrees.

Possible Answers:

$180^\circ$

$55^\circ$

$30^\circ$

$60^\circ$

$90^\circ$

Correct answer:

$90^\circ$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ .

So,

$\frac{\pi}{2}*\frac{180}{\pi}=90^\circ$ .

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Example Question #36 : Radians

Convert $\pi$ into degrees.

Possible Answers:

$3.14^{\circ}$

$90^{\circ}$

$360^{\circ}$

$30^{\circ}$

$180^{\circ}$

Correct answer:

$180^{\circ}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$\pi*\frac{180}{\pi}=180^{\circ}$ .

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Example Question #37 : Radians

Convert $7\pi$ into degrees.

Possible Answers:

$1000^{\circ}$

$1260^{\circ}$

$1200^{\circ}$

$90^{\circ}$

$1500^{\circ}$

Correct answer:

$1260^{\circ}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that, $360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$7\pi*\frac{180}{\pi}=1260^{\circ}$ .

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Example Question #38 : Radians

Convert $\frac{4\pi}{3}$ into degrees.

Possible Answers:

$240^{\circ}$

$200^{\circ}$

$250^{\circ}$

$248^{\circ}$

$100^{\circ}$

Correct answer:

$240^{\circ}$

Explanation:

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$\frac{4\pi}{3}*\frac{180}{\pi}=240^{\circ}$ .

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Example Question #39 : Radians

Convert $\frac{9\pi}{5}$ into degrees.

Possible Answers:

$159^{\circ}$

$333^{\circ}$

$324^{\circ}$

$300^{\circ}$

$355^{\circ}$

Correct answer:

$324^{\circ}$

Explanation:

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$\frac{9\pi}{5}*\frac{180}{\pi}=324^{\circ}$ .

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Example Question #31 : Radians And Conversions

Convert $-\frac{\pi}{3}$ into degrees.

Possible Answers:

$-60^{\circ}$

$180^{\circ}$

$-30^{\circ}$

$60^{\circ}$

$-90^{\circ}$

Correct answer:

$-60^{\circ}$

Explanation:

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$-\frac{\pi}{3}*\frac{180}{\pi}=-60^{\circ}$ .

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Example Question #41 : Circles

Convert $75^\circ$ into radians

Possible Answers:

$\frac {5\pi}{6}$

$-\frac {5\pi}{12}$

$\frac {5\pi}{12}$

$\frac {5\pi}{18}$

Correct answer:

$\frac {5\pi}{12}$

Explanation:

Step 1: Recall the formula to change a degree measure into radians:

The formula is: $Degree\cdot \frac {\pi}{180}$ .

Step 2: Plug in the angle:

$75 \cdot \frac {\pi}{180}$

Step 3: Simplify:

We will use the and try to reduce the 180 as much as possible.

After Dividing by 3:

$25 \cdot \frac {\pi}{60}$

After dividing by 5:

$5 \cdot \frac {\pi}{12}=\frac {5\pi}{12}$

$75^\circ$ is $\frac {5\pi}{12}$ in radians.

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Trigonometry : Radians and Conversions

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #31 : Circles

Example Question #591 : New Sat

Example Question #34 : Radians

Example Question #31 : Radians And Conversions

Example Question #36 : Radians

Example Question #37 : Radians

Example Question #38 : Radians

Example Question #39 : Radians

Example Question #31 : Radians And Conversions

Example Question #41 : Circles

All Trigonometry Resources

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