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High School Math : Trigonometry

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Example Questions

Example Question #1791 : High School Math

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

Possible Answers:

$160^{\circ}$ $\displaystyle 160^{\circ}$

$480^{\circ}$ $\displaystyle 480^{\circ}$

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

$380^{\circ}$ $\displaystyle 380^{\circ}$

$560^{\circ}$ $\displaystyle 560^{\circ}$

Correct answer:

$480^{\circ}$ $\displaystyle 480^{\circ}$

Explanation:

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

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Example Question #26 : Understanding Radians And Conversions

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

Possible Answers:

$8.03\: rad$ $\displaystyle 8.03\: rad$

$2.56\: rad$ $\displaystyle 2.56\: rad$

$6.44\: rad$ $\displaystyle 6.44\: rad$

$0.81\: rad$ $\displaystyle 0.81\: rad$

$2.46\: rad$ $\displaystyle 2.46\: rad$

Correct answer:

$8.03\: rad$ $\displaystyle 8.03\: rad$

Explanation:

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

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

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

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

$2.56\pi \ rad=x$ $\displaystyle 2.56\pi \ rad=x$

$8.03\ rad=x$ $\displaystyle 8.03\ rad=x$

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Example Question #27 : Understanding Radians And Conversions

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

Possible Answers:

$150^\circ$ $\displaystyle 150^\circ$

$54^\circ$ $\displaystyle 54^\circ$

$216^\circ$ $\displaystyle 216^\circ$

$300^\circ$ $\displaystyle 300^\circ$

$108^\circ$ $\displaystyle 108^\circ$

Correct answer:

$300^\circ$ $\displaystyle 300^\circ$

Explanation:

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

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

Cross multipy.

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

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

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

$x^\circ=300^\circ$ $\displaystyle x^\circ=300^\circ$

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Example Question #61 : Trigonometry

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

Possible Answers:

$270^\circ$ $\displaystyle 270^\circ$

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

$120^\circ$ $\displaystyle 120^\circ$

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

$240^\circ$ $\displaystyle 240^\circ$

Correct answer:

$120^\circ$ $\displaystyle 120^\circ$

Explanation:

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

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

Cross multipy:

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

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

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

$x^\circ=120^\circ$ $\displaystyle x^\circ=120^\circ$

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Example Question #34 : The Unit Circle And Radians

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

Possible Answers:

$1256.6\ radians$ $\displaystyle 1256.6\ radians$

$0.628\ radians$ $\displaystyle 0.628\ radians$

$1.26\ radians$ $\displaystyle 1.26\ radians$

$4.125\ radians$ $\displaystyle 4.125\ radians$

$4125.29\ radians$ $\displaystyle 4125.29\ radians$

Correct answer:

$1.26\ radians$ $\displaystyle 1.26\ radians$

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:

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

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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 #1792 : High School Math

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:

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

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

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

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

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

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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High School Math : Trigonometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1791 : High School Math

Example Question #26 : Understanding Radians And Conversions

Example Question #27 : Understanding Radians And Conversions

Example Question #61 : Trigonometry

Example Question #34 : The Unit Circle And Radians

Example Question #41 : The Unit Circle And Radians

Example Question #62 : Trigonometry

Example Question #1792 : High School Math

Example Question #62 : Trigonometry

Example Question #65 : Trigonometry

All High School Math Resources

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