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High School Math : Understanding Radians and Conversions

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Example Questions

Example Question #41 : The Unit Circle And Radians

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

Possible Answers:

$1.18\ rad$ $\displaystyle 1.18\ rad$

$2.37\ rad$ $\displaystyle 2.37\ rad$

$7.79\ rad$ $\displaystyle 7.79\ rad$

$136\ rad$ $\displaystyle 136\ rad$

$23.7\ rad$ $\displaystyle 23.7\ rad$

Correct answer:

$2.37\ rad$ $\displaystyle 2.37\ rad$

Explanation:

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

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

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

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

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Example Question #62 : Trigonometry

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

Possible Answers:

$0.56\ rad$ $\displaystyle 0.56\ rad$

$0.79\ rad$ $\displaystyle 0.79\ rad$

$3.14\ rad$ $\displaystyle 3.14\ rad$

$4.71\ rad$ $\displaystyle 4.71\ rad$

$1.57\ rad$ $\displaystyle 1.57\ rad$

Correct answer:

$0.79\ rad$ $\displaystyle 0.79\ rad$

Explanation:

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

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

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

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

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Example Question #63 : Trigonometry

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

Possible Answers:

$3.27\ rad$ $\displaystyle 3.27\ rad$

$2.40\ rad$ $\displaystyle 2.40\ rad$

$4.80\ rad$ $\displaystyle 4.80\ rad$

$9.60\ rad$ $\displaystyle 9.60\ rad$

$1.37\ rad$ $\displaystyle 1.37\ rad$

Correct answer:

$4.80\ rad$ $\displaystyle 4.80\ rad$

Explanation:

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

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

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

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

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Example Question #62 : Trigonometry

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

Possible Answers:

$0.86\ rad$ $\displaystyle 0.86\ rad$

$1.27\ rad$ $\displaystyle 1.27\ rad$

$3.14\ rad$ $\displaystyle 3.14\ rad$

$1.71\ rad$ $\displaystyle 1.71\ rad$

$3.42\ rad$ $\displaystyle 3.42\ rad$

Correct answer:

$1.71\ rad$ $\displaystyle 1.71\ rad$

Explanation:

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

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

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

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

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Example Question #65 : Trigonometry

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

Possible Answers:

$4\pi\,radians$ $\displaystyle 4\pi\,radians$

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

$\pi\,radians$ $\displaystyle \pi\,radians$

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

$2\pi\,radians$ $\displaystyle 2\pi\,radians$

Correct answer:

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

Explanation:

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

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

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

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

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Example Question #71 : Trigonometry

If an angle is 2.43 radians, what is the equivalent angle in degrees?

Possible Answers:

$139.23^{\circ}$ $\displaystyle 139.23^{\circ}$

$127^{\circ}$ $\displaystyle 127^{\circ}$

$45^{\circ}$ $\displaystyle 45^{\circ}$

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

$145^{\circ}$ $\displaystyle 145^{\circ}$

Correct answer:

$139.23^{\circ}$ $\displaystyle 139.23^{\circ}$

Explanation:

To answer this question, it is important to remember the relationship:

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

From here, we can set up the following formula:

$2.43\,rad\cdot \frac{180^\circ}{\pi\,rad} = 139.23^{\circ}$ $\displaystyle 2.43\,rad\cdot \frac{180^\circ}{\pi\,rad} = 139.23^{\circ}$

Multiplying across, we see that the units of radians cancel out and we are left with units in degrees.

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Example Question #71 : Trigonometry

If an angle equals 5.75 radians, what is the equivalent angle in degrees?

Possible Answers:

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

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

$329.45^{\circ}$ $\displaystyle 329.45^{\circ}$

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

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

Correct answer:

$329.45^{\circ}$ $\displaystyle 329.45^{\circ}$

Explanation:

To answer this question, it is important to remember the relationship:

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

From here, we can set up the following formula:

$5.75\,rad\cdot \frac{180^\circ}{\pi\,rad} = 329.45^{\circ}$ $\displaystyle 5.75\,rad\cdot \frac{180^\circ}{\pi\,rad} = 329.45^{\circ}$

Multiplying across, we see that the units of radians cancel out and we are left with units in degrees.

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Example Question #33 : Understanding Radians And Conversions

If an angle equals 15.71 radians, what is the equivalent angle in degrees?

Possible Answers:

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

$670^{\circ}$ $\displaystyle 670^{\circ}$

$900^{\circ}$ $\displaystyle 900^{\circ}$

$45^{\circ}$ $\displaystyle 45^{\circ}$

$1.57^{\circ}$ $\displaystyle 1.57^{\circ}$

Correct answer:

$900^{\circ}$ $\displaystyle 900^{\circ}$

Explanation:

To answer this question, it is important to remember the relationship:

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

From here, we can set up the following formula:

$15.71\,rad\cdot \frac{180^\circ}{\pi\,rads} = 900^{\circ}$ $\displaystyle 15.71\,rad\cdot \frac{180^\circ}{\pi\,rads} = 900^{\circ}$

Multiplying across, we see that the units of radians cancel out and we are left with units in degrees.

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Example Question #43 : The Unit Circle And Radians

If an angle equals 6.4 radians, what is the equivalent angle in degrees?

Possible Answers:

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

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

$366.69^{\circ}$ $\displaystyle 366.69^{\circ}$

$31.4^{\circ}$ $\displaystyle 31.4^{\circ}$

$5.78^{\circ}$ $\displaystyle 5.78^{\circ}$

Correct answer:

$366.69^{\circ}$ $\displaystyle 366.69^{\circ}$

Explanation:

To answer this question, it is important to remember the relationship:

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

From here, we can set up the following formula:

$6.4\,rad\cdot \frac{180^\circ}{\pi\,rads}= 366.69^{\circ}$ $\displaystyle 6.4\,rad\cdot \frac{180^\circ}{\pi\,rads}= 366.69^{\circ}$

Multiplying across, we see that the units of radians cancel out and we are left with units in degrees.

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Example Question #44 : The Unit Circle And Radians

If an angle is 3.55 radians, what is the equivalent angle in degrees?

Possible Answers:

$203.40^{\circ}$ $\displaystyle 203.40^{\circ}$

$270.45^{\circ}$ $\displaystyle 270.45^{\circ}$

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

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

$146.87^{\circ}$ $\displaystyle 146.87^{\circ}$

Correct answer:

$203.40^{\circ}$ $\displaystyle 203.40^{\circ}$

Explanation:

To answer this question, it is important to remember the relationship:

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

From here, we can set up the following formula:

$3.55\,rad\cdot \frac{180^\circ}{\pi\,rad} = 203.40^{\circ}$ $\displaystyle 3.55\,rad\cdot \frac{180^\circ}{\pi\,rad} = 203.40^{\circ}$

Multiplying across, we see that the units of radians cancel out and we are left with units in degrees.

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High School Math : Understanding Radians and Conversions

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #41 : The Unit Circle And Radians

Example Question #62 : Trigonometry

Example Question #63 : Trigonometry

Example Question #62 : Trigonometry

Example Question #65 : Trigonometry

Example Question #71 : Trigonometry

Example Question #71 : Trigonometry

Example Question #33 : Understanding Radians And Conversions

Example Question #43 : The Unit Circle And Radians

Example Question #44 : The Unit Circle And Radians

All High School Math Resources

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