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High School Math : Understanding Radians and Conversions

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Example Questions

Example Question #51 : The Unit Circle And Radians

If an angle is $\frac{\pi}{3}$ radians , what is the equivalent angle in degrees?

Possible Answers:

$90^{\circ}$

$60^{\circ}$

$160^{\circ}$

$180^{\circ}$

$270^{\circ}$

Correct answer:

$60^{\circ}$

Explanation:

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

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

From here, we can set up the following formula:

$\frac{\pi}{3}\,rad\cdot \frac{180^\circ}{\pi\,rad} = \frac{\180^\circ}{3} = 60^\circ$

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 #52 : The Unit Circle And Radians

How many radians are in $34^{\circ}$ ?

Possible Answers:

$\frac{17}{19}\pi$

$\frac{19}{17}\pi$

$\frac{2}{19}\pi$

$\frac{1}{2}\pi$

$\frac{34}{90}\pi$

Correct answer:

$\frac{17}{19}\pi$

Explanation:

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

$\frac{34^\circ}{x}=\frac{180^\circ}{\pi}$

$180^\circ*x=34^\circ*\pi$

$x=\frac{34^\circ*\pi}{180^\circ}$

$x=\frac{17}{19}\pi$

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Example Question #51 : The Unit Circle And Radians

Bob manages a pizza store. He bought a new machine that tracks how big his employees are cutting the pizza slices. The machine measures the average angle size of each slice of each pizza. Unfortunately, the angle is given as 0.7854 radians which Bob does not understand. Help Bob by converting the radian angle into degrees. In degrees, what is the size of the angle for an average pizza slice.

Possible Answers:

$75^{\circ}$

$60^{\circ}$

$30^{\circ}$

$25^{\circ}$

$45^{\circ}$

Correct answer:

$45^{\circ}$

Explanation:

To convert we use a common conversion amount. It may be easiest to remember the full circle example. In degrees, a full circle is $360^{\circ}$ around. In terms of radians, a full circle is $2\pi$ . So to get our answer

$0.7854\ \text{Radians} *\frac{360^{\circ}}{2\pi\ \text{Radians}}= 45^{\circ}$

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Example Question #51 : The Unit Circle And Radians

Convert $120^{\circ}$ into radians.

Possible Answers:

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

$2\pi$

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

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

$\pi$

Correct answer:

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

Explanation:

To convert from degrees to radians, one multiplies by $\frac{\pi }{180}$ .

$120\cdot \frac{\pi }{180}=\frac{2\pi}{3}$

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Example Question #53 : The Unit Circle And Radians

How many radians are in $44^\circ$ ?

Possible Answers:

$2.2\pi$

$0.24\pi$

$0.41\pi$

$4.1\pi$

$0.01\pi$

Correct answer:

$0.24\pi$

Explanation:

The ratio of degrees to radians is $\frac{180^\circ}{\pi}$ .

Set our proportions equal to each other:

$\frac{44^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply:

$44^\circ\pi=180^\circ*x$

$\frac{44^\circ}{180^\circ}*\pi=x$

$0.24\pi=x$

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Example Question #43 : Understanding Radians And Conversions

How many radians are in $208^\circ$ ?

Possible Answers:

$1.39\pi$

$1.15\pi$

$1.07\pi$

$1.67\pi$

$1.11\pi$

Correct answer:

$1.15\pi$

Explanation:

To convert degrees to radians, set up a ratio. The ratio of degrees to radians is $\frac{180^\circ}{\pi}$ .

$\frac{208^\circ}{x}=\frac{180^\circ}{\pi}$

Cross multiply.

$208^\circ*\pi=180^\circ*x$

$\frac{208^\circ}{180^\circ}*\pi=x$

$1.15\pi=x$

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Example Question #54 : The Unit Circle And Radians

How many radians are in $313^\circ$ ?

Possible Answers:

$2.11\pi$

$1.74\pi$

$0.56\pi$

$3.48\pi$

$1.05\pi$

Correct answer:

$1.74\pi$

Explanation:

To solve this, use a proportion. The ratio of degrees to radians is $\frac{180^\circ}{\pi}$ .

$\frac{313^\circ}{x}=\frac{180^\circ }{\pi}$

Cross multiply:

$313^\circ \pi=180^\circ x$

$\frac{313^\circ}{180^\circ }\pi=x$

$1.74\pi=x$

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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 #51 : The Unit Circle And Radians

Example Question #52 : The Unit Circle And Radians

Example Question #51 : The Unit Circle And Radians

Example Question #51 : The Unit Circle And Radians

Example Question #53 : The Unit Circle And Radians

Example Question #43 : Understanding Radians And Conversions

Example Question #54 : The Unit Circle And Radians

All High School Math Resources

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