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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 #583 : New Sat

Convert to radians: 33^o

Possible Answers:

0.189

0.183

0.058

1.736

0.576

Correct answer:

0.576

Explanation:

To convert to radians, set up the ratio $\frac{180}{\pi } = \frac{33} { x}$ :

$180 x = 33 \pi$

$x = 33 \pi \div 180 \approx 0.576$

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Example Question #584 : New Sat

Convert to degrees: $\frac{2 \pi }{7}$

Possible Answers:

147.58^o

51.43^o

16.37^o

0.016^o

Correct answer:

51.43^o

Explanation:

To convert, divide by $\pi$ and multiply by 180 :

$\frac{2 \pi }{7 } \div \pi = \frac{2}{7}$

$\frac{2}{7} \cdot 180 \approx 51.47^o$

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Example Question #195 : New Sat Math Calculator

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

Possible Answers:

$350^\circ$

$370^\circ$

$10^\circ$

$185^\circ$

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 #591 : New Sat

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

Possible Answers:

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

$\frac{\pi}{6}$

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

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

$\frac{\pi}{4}$

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 #592 : New Sat

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

Possible Answers:

$\frac{\pi}{3}$

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

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

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

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

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 #31 : Circles

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

Possible Answers:

$\frac{\pi}{180}$

$\frac{\pi}{360}$

$\pi$

$\frac{\pi}{90}$

$2\pi$

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 #425 : Trigonometry

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

Possible Answers:

$2\pi$

$\frac{\pi}{180}$

$\pi$

$\frac{\pi}{90}$

$\frac{\pi}{360}$

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 #593 : New Sat

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

Possible Answers:

$\frac{\pi}{18}$

$\frac{\pi}{36}$

$\frac{\pi}{180}$

$\frac{\pi}{90}$

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

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 #41 : Unit Circle And Radians

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

Possible Answers:

$\frac{\pi}{5}$

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

$3\pi$

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

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

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 #428 : Trigonometry

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

Possible Answers:

$55^\circ$

$60^\circ$

$180^\circ$

$30^\circ$

$90^\circ$

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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Trigonometry : Trigonometry

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #583 : New Sat

Example Question #584 : New Sat

Example Question #195 : New Sat Math Calculator

Example Question #591 : New Sat

Example Question #592 : New Sat

Example Question #31 : Circles

Example Question #425 : Trigonometry

Example Question #593 : New Sat

Example Question #41 : Unit Circle And Radians

Example Question #428 : Trigonometry

All Trigonometry Resources

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