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Trigonometry : Radians and Conversions

Study concepts, example questions & explanations for Trigonometry

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6 Diagnostic Tests 155 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #401 : Trigonometry

Change $\frac{\pi}{5}$ angle to degrees.

Possible Answers:

$34^{\circ}$

$30^{\circ}$

$45^{\circ}$

$32^{\circ}$

$36^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

In order to change radians to degrees, we need to multiply the radian agle measure by $\frac{180^{\circ}}{\pi}$ .

$\frac{\pi}{5}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{5}=36^{\circ}$

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Example Question #182 : New Sat Math Calculator

An angle of 40 radians is equal to how many degrees?

Possible Answers:

$\frac{7000^{\circ}}{\pi}$

$\frac{720^{\circ}}{\pi}$

$\frac{5400^{\circ}}{\pi}$

$\frac{7200^{\circ}}{\pi}$

$\frac{3600^{\circ}}{\pi}$

Correct answer:

$\frac{7200^{\circ}}{\pi}$

Explanation:

We know that one radian is equal to $\frac{180^{\circ}}{\pi}$ , so in order to change radians to degrees we need to multiply by $\frac{180^{\circ}}{\pi}$ .

$40\times \frac{180^{\circ}}{\pi}=\frac{7200^{\circ}}{\pi}$

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Example Question #402 : Trigonometry

Change $\frac{17\pi}{5}$ angle to degrees.

Possible Answers:

$712^{\circ}$

$612^{\circ}$

$512^{\circ}$

$412^{\circ}$

$620^{\circ}$

Correct answer:

$612^{\circ}$

Explanation:

In order to change radians to degrees we need to multiply the radians by $\frac{180^{\circ}}{\pi}$ .

$\frac{17\pi}{5}\times \frac{180^{\circ}}{\pi}=\frac{17\times 180^{\circ}}{5}=612^{\circ}$

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Example Question #403 : Trigonometry

Change $75^{\circ}$ to radians.

Possible Answers:

$\frac{7\pi}{12}$

$\frac{\pi}{2}$

$\frac{5\pi}{12}$

$\frac{\pi}{12}$

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

Correct answer:

$\frac{5\pi}{12}$

Explanation:

In order to change degrees to radians we need to multiply the degrees by $\frac{\pi}{180^{\circ}}$ .

$75^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{5\pi}{12}$

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Example Question #11 : Radians And Conversions

Change the following expression to degrees:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}$

Possible Answers:

$60^{\circ}$

$90^{\circ}$

$75^{\circ}$

$120^{\circ}$

$160^{\circ}$

Correct answer:

$60^{\circ}$

Explanation:

First we need to simplify the expression:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}=\frac{\frac{2\pi-\pi}{6}}{\frac{2+1}{6}}=\frac{\pi}{3}$

Now multiply by $\frac{180^{\circ}}{\pi}$ :

$\frac{\pi}{3}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{3}=60^{\circ}$

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Example Question #21 : Unit Circle And Radians

Change the following expression to degrees:

${\frac{\pi}{4}-\frac{\pi}{12}}$

Possible Answers:

$90^{\circ}$

$75^{\circ}$

$45^{\circ}$

$60^{\circ}$

$30^{\circ}$

Correct answer:

$30^{\circ}$

Explanation:

First we need to simplify the expression:

${\frac{\pi}{4}-\frac{\pi}{12}}=\frac{3\pi-\pi}{12}=\frac{2\pi}{12}=\frac{\pi}{6}$

Then multiply the radians by $\frac{180^{\circ}}{\pi}$ :

$\frac{\pi}{6}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{6}=30^{\circ}$

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Example Question #16 : Circles

Convert the following expression to radians:

$\frac{45^{\circ}+30^{\circ}}{45-30}$

Possible Answers:

$\frac{\pi}{36}$

$\frac{5\pi}{36}$

$\frac{\pi}{30}$

$\frac{\pi}{12}$

$\frac{7\pi}{36}$

Correct answer:

$\frac{\pi}{36}$

Explanation:

First we need to simplify the expression:

$\frac{45^{\circ}+30^{\circ}}{45-30}=\frac{75^{\circ}}{15}=5^{\circ}$

In order to change degrees to radians, we need to multiply by $\frac{\pi}{180^{\circ}}$ :

$5^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{36}$

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Example Question #11 : Radians

Change $270^{\circ}$ to radians.

Possible Answers:

$3\pi$

$2\pi$

$2.5\pi$

$1.5\pi$

$\pi$

Correct answer:

$1.5\pi$

Explanation:

In order to change degrees to radians we need to multiply degrees by $\frac{\pi}{180^{\circ}}$ :

$270^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{3\pi}{2}=1.5\pi$

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Example Question #12 : Radians

Convert one radian to degrees.

Possible Answers:

$50^{\circ}$

$57.3^{\circ}$

$60^{\circ}$

$47.3^{\circ}$

$67.3^{\circ}$

Correct answer:

$57.3^{\circ}$

Explanation:

In order to change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ :

$1\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{\pi}\approx 57.3^{\circ}$

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Example Question #31 : Unit Circle And Radians

Convert one degree to radians.

Possible Answers:

$\frac{\pi}{180}$

$\frac{\pi}{60}$

$\pi$

$\frac{\pi}{120}$

$\frac{\pi}{90}$

Correct answer:

$\frac{\pi}{180}$

Explanation:

In order to change degrees to radians we need to multiply the degrees by $\frac{\pi}{180^{\circ}}$ :

$1^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{\pi}{180}$

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Trigonometry : Radians and Conversions

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #401 : Trigonometry

Example Question #182 : New Sat Math Calculator

Example Question #402 : Trigonometry

Example Question #403 : Trigonometry

Example Question #11 : Radians And Conversions

Example Question #21 : Unit Circle And Radians

Example Question #16 : Circles

Example Question #11 : Radians

Example Question #12 : Radians

Example Question #31 : Unit Circle And Radians

All Trigonometry Resources

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