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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 #22 : Circles

Convert to radians: 33^o $\displaystyle 33^o$

Possible Answers:

0.183 $\displaystyle 0.183$

0.576 $\displaystyle 0.576$

0.058 $\displaystyle 0.058$

1.736 $\displaystyle 1.736$

0.189 $\displaystyle 0.189$

Correct answer:

0.576 $\displaystyle 0.576$

Explanation:

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

$180 x = 33 \pi$ $\displaystyle 180 x = 33 \pi$

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

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Example Question #23 : Circles

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

Possible Answers:

16.37^o $\displaystyle 16.37^o$

51.43^o $\displaystyle 51.43^o$

0.016^o $\displaystyle 0.016^o$

$\displaystyle 147.58^o$

Correct answer:

51.43^o $\displaystyle 51.43^o$

Explanation:

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

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

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

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Example Question #24 : Circles

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

Possible Answers:

$350^\circ$ $\displaystyle 350^\circ$

$10^\circ$ $\displaystyle 10^\circ$

$370^\circ$ $\displaystyle 370^\circ$

$185^\circ$ $\displaystyle 185^\circ$

Correct answer:

$370^\circ$ $\displaystyle 370^\circ$

Explanation:

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

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

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Example Question #28 : Circles

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

Possible Answers:

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

$\frac{\pi}{4}$ $\displaystyle \frac{\pi}{4}$

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

$\frac{\pi}{6}$ $\displaystyle \frac{\pi}{6}$

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

Correct answer:

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

Explanation:

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

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

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

So in this particular case,

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

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Example Question #29 : Circles

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

Possible Answers:

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

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

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

$\frac{\pi}{3}$ $\displaystyle \frac{\pi}{3}$

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

Correct answer:

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

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

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

So in this particular case,

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

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Example Question #42 : Unit Circle And Radians

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

Possible Answers:

$\frac{\pi}{90}$ $\displaystyle \frac{\pi}{90}$

$\frac{\pi}{360}$ $\displaystyle \frac{\pi}{360}$

$2\pi$ $\displaystyle 2\pi$

$\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

$\pi$ $\displaystyle \pi$

Correct answer:

$\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

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,

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

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

So in this particular case,

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

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Example Question #592 : New Sat

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

Possible Answers:

$\frac{\pi}{90}$ $\displaystyle \frac{\pi}{90}$

$\pi$ $\displaystyle \pi$

$2\pi$ $\displaystyle 2\pi$

$\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

$\frac{\pi}{360}$ $\displaystyle \frac{\pi}{360}$

Correct answer:

$\frac{\pi}{90}$ $\displaystyle \frac{\pi}{90}$

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,

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

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

So in this particular case,

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

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Example Question #43 : Unit Circle And Radians

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

Possible Answers:

$\frac{\pi}{90}$ $\displaystyle \frac{\pi}{90}$

$\frac{\pi}{36}$ $\displaystyle \frac{\pi}{36}$

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

$\frac{\pi}{18}$ $\displaystyle \frac{\pi}{18}$

$\frac{\pi}{180}$ $\displaystyle \frac{\pi}{180}$

Correct answer:

$\frac{\pi}{18}$ $\displaystyle \frac{\pi}{18}$

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,

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

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

So in this particular case,

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

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Example Question #44 : Unit Circle And Radians

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

Possible Answers:

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

$\frac{\pi}{5}$ $\displaystyle \frac{\pi}{5}$

$3\pi$ $\displaystyle 3\pi$

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

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

Correct answer:

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

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,

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

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

So in this particular case,

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

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Example Question #421 : Trigonometry

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

Possible Answers:

$180^\circ$ $\displaystyle 180^\circ$

$90^\circ$ $\displaystyle 90^\circ$

$60^\circ$ $\displaystyle 60^\circ$

$55^\circ$ $\displaystyle 55^\circ$

$30^\circ$ $\displaystyle 30^\circ$

Correct answer:

$90^\circ$ $\displaystyle 90^\circ$

Explanation:

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

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

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

So,

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

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Trigonometry : Trigonometry

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #22 : Circles

Example Question #23 : Circles

Example Question #24 : Circles

Example Question #28 : Circles

Example Question #29 : Circles

Example Question #42 : Unit Circle And Radians

Example Question #592 : New Sat

Example Question #43 : Unit Circle And Radians

Example Question #44 : Unit Circle And Radians

Example Question #421 : Trigonometry

All Trigonometry Resources

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