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High School Math : Trigonometry

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Example Questions

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Example Question #61 : Trigonometry

Convert $\frac{8\pi }{3}$ to degrees.

Possible Answers:

$560^{\circ}$

$160^{\circ}$

$480^{\circ}$

$360^{\circ}$

$380^{\circ}$

Correct answer:

$480^{\circ}$

Explanation:

Multiply by $\frac{180}{\pi }$ and then simplify. The answer is $480^{\circ}$ .

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Example Question #27 : Understanding Radians And Conversions

How many radians are in $230^\circ$ ?

Possible Answers:

$8.03\: rad$

$2.56\: rad$

$6.44\: rad$

$2.46\: rad$

$0.81\: rad$

Correct answer:

$8.03\: rad$

Explanation:

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

$\frac{230^\circ}{x}=\frac{180^\circ}{2\pi \, rad}$

$230^\circ*2\pi \ rad=180^\circ*x$

$\frac{230^\circ*2\pi \ rad}{180^\circ}=x$

$2.56\pi \ rad=x$

$8.03\ rad=x$

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Example Question #28 : Understanding Radians And Conversions

How many degrees are in $\frac{5}{3}\pi$ radians?

Possible Answers:

$108^\circ$

$54^\circ$

$300^\circ$

$150^\circ$

$216^\circ$

Correct answer:

$300^\circ$

Explanation:

The conversion between radians and degrees is $\pi={180^\circ}$ . We can use this as a ratio to solve:

$\frac{\frac{5}{3}\pi}{x^\circ}=\frac{\pi}{180^\circ}$

Cross multipy.

$x^\circ*\pi=\frac{5}{3}\pi *180^\circ$

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

$x^\circ=\frac{5}{3} *180^\circ$

$x^\circ=300^\circ$

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Example Question #29 : Understanding Radians And Conversions

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

Possible Answers:

$180^\circ$

$120^\circ$

$60^\circ$

$270^\circ$

$240^\circ$

Correct answer:

$120^\circ$

Explanation:

The conversion between radians and degrees is $\pi={180^\circ}$ . We can then create a ratio to solve:

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

Cross multipy:

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

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

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

$x^\circ=120^\circ$

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Example Question #30 : Understanding Radians And Conversions

If Angle equals $72^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

Possible Answers:

$1256.6\ radians$

$0.628\ radians$

$4.125\ radians$

$1.26\ radians$

$4125.29\ radians$

Correct answer:

$1.26\ radians$

Explanation:

To convert between radians and degrees, it is important to remember that:

$\pi\, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$72^{\circ}\cdot \frac{\pi}{180^{\circ}} = 1.26\,rad$

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Example Question #41 : The Unit Circle And Radians

If angle equals $136^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

Possible Answers:

$23.7\ rad$

$7.79\ rad$

$1.18\ rad$

$136\ rad$

$2.37\ rad$

Correct answer:

$2.37\ rad$

Explanation:

To convert between radians and degrees, it is important to remember that:

$\pi\, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$136^{\circ}\cdot \frac{\pi}{180^{\circ}} = 2.37\,rad$

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Example Question #42 : The Unit Circle And Radians

If $\angle A$ equals $45^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

Possible Answers:

$1.57\ rad$

$0.56\ rad$

$3.14\ rad$

$4.71\ rad$

$0.79\ rad$

Correct answer:

$0.79\ rad$

Explanation:

To convert between radians and degrees, it is important to remember that:

$\pi\, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$45^{\circ}\cdot \frac{\pi}{180^{\circ}} = 0.79\,rad$

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Example Question #43 : The Unit Circle And Radians

If $\angle B$ is $275^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

Possible Answers:

$3.27\ rad$

$9.60\ rad$

$2.40\ rad$

$1.37\ rad$

$4.80\ rad$

Correct answer:

$4.80\ rad$

Explanation:

To convert between radians and degrees, it is important to remember that:

$\pi\, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$275^{\circ}\cdot \frac{\pi}{180^{\circ}} = 4.80\,rad$

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Example Question #44 : The Unit Circle And Radians

If an angle is $98^{\circ}$ , what is the equivalent angle in radians (to the nearest hundredth)?

Possible Answers:

$0.86\ rad$

$3.42\ rad$

$3.14\ rad$

$1.27\ rad$

$1.71\ rad$

Correct answer:

$1.71\ rad$

Explanation:

To convert between radians and degrees, it is important to remember that:

$\pi\, rad = 180^{\circ}$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$98^{\circ}\cdot \frac{\pi}{180^{\circ}}= 1.71\,rad$

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Example Question #45 : The Unit Circle And Radians

What angle below is equivalent to $90^{\circ}$ ?

Possible Answers:

$4\pi\,radians$

$\frac{\pi}{2}\,radians$

$2\pi\,radians$

$\frac{\pi}{4}\,radians$

$\pi\,radians$

Correct answer:

$\frac{\pi}{2}\,radians$

Explanation:

To convert between radians and degrees, it is important to remember that:

$\pi\, radians = 180\, degrees$

With this relationship in mind, we can convert from degrees to radians with the following formula:

$90^{\circ}\cdot \frac{\pi}{180^{\circ}} = \frac{1}{2}\cdot \pi = \frac{\pi}{2}\,radians$

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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 #61 : Trigonometry

Example Question #27 : Understanding Radians And Conversions

Example Question #28 : Understanding Radians And Conversions

Example Question #29 : Understanding Radians And Conversions

Example Question #30 : Understanding Radians And Conversions

Example Question #41 : The Unit Circle And Radians

Example Question #42 : The Unit Circle And Radians

Example Question #43 : The Unit Circle And Radians

Example Question #44 : The Unit Circle And Radians

Example Question #45 : The Unit Circle And Radians

All High School Math Resources

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