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High School Math : Trigonometry

Study concepts, example questions & explanations for High School Math

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Example Questions

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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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Example Question #51 : Trigonometry

How many degrees are in $3\pi$ radians?

Possible Answers:

$180^\circ$

$340^\circ$

$540^\circ$

$510^\circ$

$460^\circ$

Correct answer:

$540^\circ$

Explanation:

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

That means we can set up a proportion:

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

$x\pi=180^\circ*3\pi$

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

$x=180^\circ*3$

$x=540^\circ$

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Example Question #51 : Trigonometry

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

Possible Answers:

$240^\circ$

$30^\circ$

$120^\circ$

$60^\circ$

$150^\circ$

Correct answer:

$120^\circ$

Explanation:

The conversion rate for degrees and radians is $\frac{180^\circ}{\pi \: rad}$ .

Set up a proportion to solve.

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

Cross multiply.

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

Notice that the $\pi$ cancels out.

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

$120^\circ=x$

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Example Question #51 : Trigonometry

How many degrees are in $2.42\pi$ radians?

Possible Answers:

$233.67^\circ$

$74.39^\circ$

$435.6^\circ$

$217.8^\circ$

$148.76^\circ$

Correct answer:

$217.8^\circ$

Explanation:

The ratio of degrees to radians is $\frac{180^\circ}{2\pi}$ . Set up a proportion and solve.

$\frac{x^\circ}{2.42\pi}=\frac{180^\circ}{2\pi}$

$x^\circ*2\pi=180^\circ*2.42\pi$

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

$x^\circ*2=180^\circ*2.42$

$x^\circ*2=435.6^\circ$

$x^\circ=\frac{435.6^\circ}{2}$

$x^\circ=217.8^\circ$

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Example Question #21 : Understanding Radians And Conversions

How many radians are in $512^\circ$ ?

Possible Answers:

$2.84\pi$

$0.70\pi$

$0.35\pi$

$1.84\pi$

$1.42\pi$

Correct answer:

$2.84\pi$

Explanation:

The relationship between degrees and radians is $180^\circ=\pi\, rads$ . We can set this up as a proportion to solve:

$\frac{512^\circ}{x}=\frac{180^\circ}{\pi}$

$512^\circ*\pi=180^\circ*x$

$\frac{512^\circ}{180^\circ}\pi=x$

$2.84\pi=x$

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Example Question #1782 : High School Math

Convert $315^{\circ}$ to radians.

Possible Answers:

$\frac{10\pi }{4}$

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

$\frac{7\pi }{4}$

$\frac{11\pi }{4}$

$\frac{7 }{4}$

Correct answer:

$\frac{7\pi }{4}$

Explanation:

Multiply the given degrees measurement by $\frac{\pi }{180}$ .

Simplify and you get $\frac{7\pi }{4}$ .

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High School Math : Trigonometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

Example Question #51 : Trigonometry

Example Question #51 : Trigonometry

Example Question #51 : Trigonometry

Example Question #21 : Understanding Radians And Conversions

Example Question #1782 : High School Math

All High School Math Resources

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