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Trigonometry : Unit Circle and Radians

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 #28 : Radians

$\frac{37\pi}{18}$ radians is equivalent to how many degrees?

Possible Answers:

$370^\circ$

$350^\circ$

$10^\circ$

$185^\circ$

Correct answer:

$370^\circ$

Explanation:

1 radian is equal to $\frac{180}{\pi}$ degrees. Using this conversion factor,

$\frac{37\pi}{18}\times\frac{180}{\pi}=37\times10=370$ .

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Example Question #29 : Radians

Convert $150^{\circ}$ into radians.

Possible Answers:

$\frac{\pi}{4}$

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

$\frac{10\pi}{6}$

$\frac{5\pi}{6}$

$\frac{\pi}{6}$

Correct answer:

$\frac{5\pi}{6}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$150*\frac{\pi}{180}=\frac{5\pi}{6}$ .

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Example Question #30 : Radians

Convert $330^{\circ}$ into radians.

Possible Answers:

$\frac{\pi}{3}$

$\frac{7\pi}{5}$

$\frac{11\pi}{6}$

$\frac{5\pi}{6}$

$\frac{7\pi}{3}$

Correct answer:

$\frac{11\pi}{6}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that, $360^\circ=2\pi \Rightarrow 180^\circ=\pi$

Thus, in order to convert from degrees to radians you need to multiply by . $\frac{\pi}{180}$

So in this particular case,

$330*\frac{\pi}{180}=\frac{11\pi}{6}$ .

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Example Question #591 : New Sat

Convert $1^{\circ}$ into radians.

Possible Answers:

$\frac{\pi}{360}$

$2\pi$

$\frac{\pi}{90}$

$\frac{\pi}{180}$

$\pi$

Correct answer:

$\frac{\pi}{180}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$1*\frac{\pi}{180}=\frac{\pi}{180}$ .

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Example Question #591 : New Sat

Convert $2^{\circ}$ into radians.

Possible Answers:

$\pi$

$\frac{\pi}{360}$

$2\pi$

$\frac{\pi}{180}$

$\frac{\pi}{90}$

Correct answer:

$\frac{\pi}{90}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$2*\frac{\pi}{180}=\frac{\pi}{90}$ .

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Example Question #592 : New Sat

Convert $10^{\circ}$ into radians.

Possible Answers:

$\frac{10\pi}{9}$

$\frac{\pi}{36}$

$\frac{\pi}{180}$

$\frac{\pi}{90}$

$\frac{\pi}{18}$

Correct answer:

$\frac{\pi}{18}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$10*\frac{\pi}{180}=\frac{\pi}{18}$ .

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Example Question #593 : New Sat

Convert $600^{\circ}$ into radians.

Possible Answers:

$\frac{11\pi}{5}$

$3\pi$

$\frac{10\pi}{3}$

$\frac{10\pi}{9}$

$\frac{\pi}{5}$

Correct answer:

$\frac{10\pi}{3}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Thus, in order to convert from degrees to radians you need to multiply by $\frac{\pi}{180}$ .

So in this particular case,

$600*\frac{\pi}{180}=\frac{10\pi}{3}$ .

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Example Question #45 : Unit Circle And Radians

Convert $\frac{\pi}{2}$ into degrees.

Possible Answers:

$55^\circ$

$30^\circ$

$180^\circ$

$60^\circ$

$90^\circ$

Correct answer:

$90^\circ$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ .

So,

$\frac{\pi}{2}*\frac{180}{\pi}=90^\circ$ .

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Example Question #594 : New Sat

Convert $\pi$ into degrees.

Possible Answers:

$30^{\circ}$

$180^{\circ}$

$360^{\circ}$

$3.14^{\circ}$

$90^{\circ}$

Correct answer:

$180^{\circ}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that,

$360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$\pi*\frac{180}{\pi}=180^{\circ}$ .

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Example Question #601 : New Sat

Convert $7\pi$ into degrees.

Possible Answers:

$1200^{\circ}$

$1260^{\circ}$

$90^{\circ}$

$1000^{\circ}$

$1500^{\circ}$

Correct answer:

$1260^{\circ}$

Explanation:

Recall that there are 360 degrees in a circle which is equivalent to $2\pi$ radians. In order to convert between radians and degrees use the relationship that, $360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

Therefore, in order to convert from radians to degrees you need to multiply by $\frac{180}{\pi}$ . So in this particular case,

$7\pi*\frac{180}{\pi}=1260^{\circ}$ .

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Trigonometry : Unit Circle and Radians

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #28 : Radians

Example Question #29 : Radians

Example Question #30 : Radians

Example Question #591 : New Sat

Example Question #591 : New Sat

Example Question #592 : New Sat

Example Question #593 : New Sat

Example Question #45 : Unit Circle And Radians

Example Question #594 : New Sat

Example Question #601 : New Sat

All Trigonometry Resources

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