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High School Math : The Unit Circle and Radians

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Example Question #41 : Trigonometry

How many degrees are in $\frac{2\pi}{3}$ radians?

Possible Answers:

$210^\circ$

$180^\circ$

$120^\circ$

$150^\circ$

$60^\circ$

Correct answer:

$120^\circ$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{x^\circ}{\frac{2\pi}{3}}=\frac{180^\circ}{\pi}$

Cross multiply:

$x^\circ*\pi=180^\circ*\frac{2\pi}{3}$

Notice that the $\pi$ 's cancel out:

$x^\circ=180^\circ*\frac{2}{3}$

$x^\circ=120^\circ$

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Example Question #42 : Trigonometry

How many degrees are in $\frac{5\pi}{6}$ radians?

Possible Answers:

$210^\circ$

$30^\circ$

$150^\circ$

$240^\circ$

$390^\circ$

Correct answer:

$150^\circ$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{x^\circ}{\frac{5\pi}{6}}=\frac{180^\circ}{\pi}$

Cross multiply:

$x^\circ*\pi=180^\circ*\frac{5\pi}{6}$

Notice that the $\pi$ 's cancel out:

$x^\circ=180^\circ*\frac{5}{6}$

$x^\circ=150^\circ$

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Example Question #43 : Trigonometry

How many radians are in $120^\circ$ ?

Possible Answers:

$\frac{2\pi}{3}$

$6\pi$

$\frac{\pi}{2}$

$2\pi$

$\frac{3\pi}{2}$

Correct answer:

$\frac{2\pi}{3}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{120^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$120^\circ*\pi=180^\circ*x$

Isolate :

$\frac{120^\circ}{180^\circ}\pi=x$

$\frac{2\pi}{3}=x$

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Example Question #44 : Trigonometry

How many radians are in $360^\circ$ ?

Possible Answers:

$2\pi$

$\frac{\pi}{2}$

$\pi^2$

$4\pi$

$\pi$

Correct answer:

$2\pi$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{360^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$360^\circ*\pi=180^\circ*x$

Isolate :

$\frac{360^\circ}{180^\circ}\pi=x$

$2\pi=x$

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Example Question #45 : Trigonometry

How many radians are in $405^\circ$ ?

Possible Answers:

$\frac{9\pi}{4}$

$\frac{\pi}{4}$

$\frac{4\pi}{9}$

$\frac{2\pi}{9}$

$\frac{3\pi}{4}$

Correct answer:

$\frac{9\pi}{4}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{405^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$405^\circ*\pi=180^\circ*x$

Isolate :

$\frac{405^\circ}{180^\circ}\pi=x$

$\frac{9\pi}{4}=x$

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Example Question #21 : The Unit Circle And Radians

How many radians are in $81^\circ$ ?

Possible Answers:

$\frac{20\pi}{9}$

$180\pi$

$\frac{9\pi}{20}$

$2\pi+9$

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

Correct answer:

$\frac{9\pi}{20}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{81^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$81^\circ*\pi=180^\circ*x$

Isolate :

$\frac{81^\circ}{180^\circ}\pi=x$

Reduce:

$\frac{9\pi}{20}=x$

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Example Question #22 : The Unit Circle And Radians

How many radians are in $90^\circ$ ?

Possible Answers:

$\frac{2\pi}{3}$

$\frac{\pi}{2}$

$2\pi$

$\frac{\pi}{4}$

$\pi$

Correct answer:

$\frac{\pi}{2}$

Explanation:

The conversion for radians is $180^\circ=\pi$ , so we can make a ratio:

$\frac{90^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$90^\circ*\pi=180^\circ*x$

Isolate :

$\frac{90^\circ}{180^\circ}\pi=x$

Reduce:

$\frac{\pi}{2}=x$

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Example Question #1781 : High School Math

How many degrees are in $2\pi$ radians?

Possible Answers:

$720^\circ$

$90^\circ$

$360^\circ$

$180^\circ$

$540^\circ$

Correct answer:

$360^\circ$

Explanation:

Remember, $180^\circ=\pi$ radians, so $2\pi$ radians would correspond to $2*180^\circ=360^\circ$ .

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Example Question #24 : The Unit Circle And Radians

How many radians are in $180^\circ$ ?

Possible Answers:

$\frac{\pi}{2}$

$\pi$

$\frac{2\pi}{3}$

$2\pi$

$\frac{3\pi}{2}$

Correct answer:

$\pi$

Explanation:

The ratio between radians and degrees is $180^\circ=\pi$ radians.

Since the question asks us about $180^\circ$ , the conversion tells us it will be $\pi$ radians.

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Example Question #25 : The Unit Circle And Radians

How many degrees are in $\frac{3}{4}\pi$ radians?

Possible Answers:

$90^\circ$

$225^\circ$

$270^\circ$

$135^\circ$

$450^\circ$

Correct answer:

$135^\circ$

Explanation:

The ratio between radians and degrees is $180^\circ=\pi$ radians.

That means we can set up a proportion:

$\frac{x}{\frac{3}{4}\pi}=\frac{180^\circ}{\pi}$

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

Notice that the $\pi$ 's cancel out.

$x=180^\circ*\frac{3}{4}$

$x=135^\circ$

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High School Math : The Unit Circle and Radians

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #41 : Trigonometry

Example Question #42 : Trigonometry

Example Question #43 : Trigonometry

Example Question #44 : Trigonometry

Example Question #45 : Trigonometry

Example Question #21 : The Unit Circle And Radians

Example Question #22 : The Unit Circle And Radians

Example Question #1781 : High School Math

Example Question #24 : The Unit Circle And Radians

Example Question #25 : The Unit Circle And Radians

All High School Math Resources

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