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Trigonometry : Radians and Conversions

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Example Questions

Example Question #31 : Radians

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

Possible Answers:

$\frac{\pi}{360}$ $\displaystyle \frac{\pi}{360}$

$\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

$\frac{\pi}{90}$ $\displaystyle \frac{\pi}{90}$

$2\pi$ $\displaystyle 2\pi$

$\pi$ $\displaystyle \pi$

Correct answer:

$\frac{\pi}{90}$ $\displaystyle \frac{\pi}{90}$

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,

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

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

So in this particular case,

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

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Example Question #32 : Circles

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

Possible Answers:

$\frac{\pi}{18}$ $\displaystyle \frac{\pi}{18}$

$\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

$\frac{\pi}{36}$ $\displaystyle \frac{\pi}{36}$

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

$\frac{\pi}{90}$ $\displaystyle \frac{\pi}{90}$

Correct answer:

$\frac{\pi}{18}$ $\displaystyle \frac{\pi}{18}$

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,

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

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

So in this particular case,

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

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Example Question #33 : Circles

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

Possible Answers:

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

$3\pi$ $\displaystyle 3\pi$

$\frac{\pi}{5}$ $\displaystyle \frac{\pi}{5}$

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

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

Correct answer:

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

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,

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

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

So in this particular case,

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

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Example Question #32 : Circles

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

Possible Answers:

$55^\circ$ $\displaystyle 55^\circ$

$60^\circ$ $\displaystyle 60^\circ$

$90^\circ$ $\displaystyle 90^\circ$

$180^\circ$ $\displaystyle 180^\circ$

$30^\circ$ $\displaystyle 30^\circ$

Correct answer:

$90^\circ$ $\displaystyle 90^\circ$

Explanation:

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

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

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

So,

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

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Example Question #34 : Circles

Convert $\pi$ $\displaystyle \pi$ into degrees.

Possible Answers:

$180^{\circ}$ $\displaystyle 180^{\circ}$

$90^{\circ}$ $\displaystyle 90^{\circ}$

$30^{\circ}$ $\displaystyle 30^{\circ}$

$3.14^{\circ}$ $\displaystyle 3.14^{\circ}$

$360^{\circ}$ $\displaystyle 360^{\circ}$

Correct answer:

$180^{\circ}$ $\displaystyle 180^{\circ}$

Explanation:

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

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

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

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

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Example Question #35 : Circles

Convert $7\pi$ $\displaystyle 7\pi$ into degrees.

Possible Answers:

$1000^{\circ}$ $\displaystyle 1000^{\circ}$

$90^{\circ}$ $\displaystyle 90^{\circ}$

$1500^{\circ}$ $\displaystyle 1500^{\circ}$

$1260^{\circ}$ $\displaystyle 1260^{\circ}$

$1200^{\circ}$ $\displaystyle 1200^{\circ}$

Correct answer:

$1260^{\circ}$ $\displaystyle 1260^{\circ}$

Explanation:

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

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

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

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Example Question #36 : Circles

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

Possible Answers:

$100^{\circ}$ $\displaystyle 100^{\circ}$

$248^{\circ}$ $\displaystyle 248^{\circ}$

$250^{\circ}$ $\displaystyle 250^{\circ}$

$200^{\circ}$ $\displaystyle 200^{\circ}$

$240^{\circ}$ $\displaystyle 240^{\circ}$

Correct answer:

$240^{\circ}$ $\displaystyle 240^{\circ}$

Explanation:

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

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

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Example Question #601 : New Sat

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

Possible Answers:

$324^{\circ}$ $\displaystyle 324^{\circ}$

$300^{\circ}$ $\displaystyle 300^{\circ}$

$355^{\circ}$ $\displaystyle 355^{\circ}$

$333^{\circ}$ $\displaystyle 333^{\circ}$

$159^{\circ}$ $\displaystyle 159^{\circ}$

Correct answer:

$324^{\circ}$ $\displaystyle 324^{\circ}$

Explanation:

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

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

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Example Question #31 : Radians And Conversions

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

Possible Answers:

$60^{\circ}$ $\displaystyle 60^{\circ}$

$180^{\circ}$ $\displaystyle 180^{\circ}$

$-30^{\circ}$ $\displaystyle -30^{\circ}$

$-90^{\circ}$ $\displaystyle -90^{\circ}$

$-60^{\circ}$ $\displaystyle -60^{\circ}$

Correct answer:

$-60^{\circ}$ $\displaystyle -60^{\circ}$

Explanation:

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

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

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Example Question #41 : Circles

Convert $75^\circ$ $\displaystyle 75^\circ$ into radians

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

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

Step 2: Plug in the angle:

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

Step 3: Simplify:

We will use the $\displaystyle 75$ and try to reduce the 180 $\displaystyle 180$ as much as possible.

After Dividing by 3:

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

After dividing by 5:

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

$75^\circ$ $\displaystyle 75^\circ$ is $\frac {5\pi}{12}$ $\displaystyle \frac {5\pi}{12}$ 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 : Radians

Example Question #32 : Circles

Example Question #33 : Circles

Example Question #32 : Circles

Example Question #34 : Circles

Example Question #35 : Circles

Example Question #36 : Circles

Example Question #601 : New Sat

Example Question #31 : Radians And Conversions

Example Question #41 : Circles

All Trigonometry Resources

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