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Trigonometry : Trigonometry

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 #14 : Circles

Change the following expression to degrees:

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

Possible Answers:

$120^{\circ}$

$75^{\circ}$

$90^{\circ}$

$60^{\circ}$

$160^{\circ}$

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 #574 : New Sat

Change the following expression to degrees:

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

Possible Answers:

$30^{\circ}$

$60^{\circ}$

$90^{\circ}$

$45^{\circ}$

$75^{\circ}$

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 #31 : Unit Circle And Radians

Convert the following expression to radians:

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

Possible Answers:

$\frac{\pi}{30}$

$\frac{\pi}{36}$

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

$\frac{\pi}{12}$

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

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 #184 : New Sat Math Calculator

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

Possible Answers:

$\pi$

$1.5\pi$

$2.5\pi$

$2\pi$

$3\pi$

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 #185 : New Sat Math Calculator

Convert one radian to degrees.

Possible Answers:

$50^{\circ}$

$67.3^{\circ}$

$47.3^{\circ}$

$57.3^{\circ}$

$60^{\circ}$

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 #581 : New Sat

Convert one degree to radians.

Possible Answers:

$\frac{\pi}{60}$

$\pi$

$\frac{\pi}{180}$

$\frac{\pi}{120}$

$\frac{\pi}{90}$

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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Example Question #21 : Radians

Simplify and give the followoing expression in degrees:

$2\pi-\frac{\pi}{4}$

Possible Answers:

$315^{\circ}$

$285^{\circ}$

$300^{\circ}$

$270^{\circ}$

$325^{\circ}$

Correct answer:

$315^{\circ}$

Explanation:

First we need to simplify the expression:

$2\pi-\frac{\pi}{4}=\frac{8\pi-\pi}{4}=\frac{7\pi}{4}$

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

$\frac{7\pi}{4}\times \frac{180^{\circ}}{\pi}=\frac{7\times 180^{\circ}}{4}=315^{\circ}$

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Example Question #21 : Circles

Simplify and give the followoing expression in degrees:

$\frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}$

Possible Answers:

$350^{\circ}$

$480^{\circ}$

$380^{\circ}$

$450^{\circ}$

$420^{\circ}$

Correct answer:

$450^{\circ}$

Explanation:

First we need to simplify the expression:

$\frac{\frac{2\pi}{7}+\frac{\pi}{14}}{\frac{1}{7}}=\frac{\frac{4\pi+\pi}{14}}{\frac{1}{7}}=\frac{5\pi}{2}$

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

$\frac{5\pi}{2}\times \frac{180^{\circ}}{\pi}=\frac{5\times 180^{\circ}}{2}=450^{\circ}$

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Example Question #582 : New Sat

Convert $\frac{2\pi}{3}$ radians to degrees.

Possible Answers:

$30^\circ$

$250^\circ$

$150^\circ$

$60^\circ$

$120^\circ$

Correct answer:

$120^\circ$

Explanation:

Use the conversion $\pi \textup{ radians}= 180\textup{ degrees}$ .

Since we are converting radians to degrees, multiply by 180 degrees and divide by $\pi$ radians.

$\frac{2\pi}{3} \textup{ radians}\left(\frac{180 \textup{ degrees}}{\pi\textup{ radian}}\right)= 120\textup{ degrees}$

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Example Question #582 : New Sat

How many degrees is 3 radians?

Possible Answers:

None of these other answers.

$189^{\circ}$

$172^{\circ}$

$150^{\circ}$

$156^{\circ}$

Correct answer:

$172^{\circ}$

Explanation:

When going from radians to degrees one multiplies by the conversion factor

$\frac{180^{\circ}}{\pi rad}$ .

The radians cancel and the answer is left in degrees.

$3\hspace{1mm}{\color{Red} rad}\cdot\frac{180^{\circ}}{\pi {\color{Red} rad}}=\frac{540^\circ}{\pi}=172^{\circ}$

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Trigonometry : Trigonometry

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #14 : Circles

Example Question #574 : New Sat

Example Question #31 : Unit Circle And Radians

Example Question #184 : New Sat Math Calculator

Example Question #185 : New Sat Math Calculator

Example Question #581 : New Sat

Example Question #21 : Radians

Example Question #21 : Circles

Example Question #582 : New Sat

Example Question #582 : New Sat

All Trigonometry Resources

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