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New SAT Math - Calculator : Circles

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Example Questions

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Example Question #21 :Radians

Simplify and give the followoing expression in degrees:

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

Possible Answers:

$285^{\circ}$

$270^{\circ}$

$300^{\circ}$

$315^{\circ}$

$325^{\circ}$

有限公司rrect 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 #22 :Radians

Simplify and give the followoing expression in degrees:

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

Possible Answers:

$480^{\circ}$

$420^{\circ}$

$350^{\circ}$

$450^{\circ}$

$380^{\circ}$

有限公司rrect 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 #23 :Radians

有限公司nvert $\frac{2\pi}{3}$ radians to degrees.

Possible Answers:

$30^\circ$

$120^\circ$

$250^\circ$

$150^\circ$

$60^\circ$

有限公司rrect 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 #24 :Radians

How many degrees is 3 radians?

Possible Answers:

$189^{\circ}$

$150^{\circ}$

None of these other answers.

$156^{\circ}$

$172^{\circ}$

有限公司rrect 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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Example Question #25 :Radians

有限公司nvert to radians: 33^o

Possible Answers:

1.736

0.058

0.576

0.189

0.183

有限公司rrect 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 #26 :Radians

有限公司nvert to degrees: $\frac{2 \pi }{7}$

Possible Answers:

0.016^o

147.58^o

16.37^o

51.43^o

有限公司rrect 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 #27 :Radians

有限公司nvert $\frac{7\pi}{4}$ radians into degrees.

Possible Answers:

$270^{\circ}$

$315^{\circ}$

$285^{\circ}$

$345^{\circ}$

$225^{\circ}$

有限公司rrect answer:

$315^{\circ}$

Explanation:

Recall the definition of "radians" derived from the unit circle:

$180^{\circ} = \pi rad$

The quantity of radians given in the problem is $\frac{7\pi}{4}$ . All that is required to convert this measure into degrees is to denote the unknown angle measure in degrees by $\Theta$ and set up a proportion equation using the aforementioned definition relating radians to degrees:

$\frac{180^{\circ}}{\Theta} = \frac{\pi rad}{\frac{7\pi}{4} rad}$

Cross-multiply the denominators in these fractions to obtain:

$1260^{\circ}\pi rad=4\Theta\pi rad$

$315^{\circ}\pi rad =\Theta\pi rad$ .

Canceling like terms in these equations yields

$\Theta = 315^{\circ}$

Hence, the correct angle measure of $\frac{7\pi}{4}$ in degrees is $315^{\circ}$ .

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Example Question #28 :Radians

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

Possible Answers:

$350^\circ$

$370^\circ$

$10^\circ$

$185^\circ$

有限公司rrect 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

有限公司nvert $150^{\circ}$ into radians.

Possible Answers:

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

$\frac{\pi}{6}$

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

$\frac{\pi}{4}$

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

有限公司rrect 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

有限公司nvert $330^{\circ}$ into radians.

Possible Answers:

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

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

$\frac{\pi}{3}$

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

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

有限公司rrect 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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New SAT Math - Calculator : Circles

Study concepts, example questions & explanations for New SAT Math - Calculator

All New SAT Math - Calculator Resources

Example Questions

Example Question #21 :Radians

Example Question #22 :Radians

Example Question #23 :Radians

Example Question #24 :Radians

Example Question #25 :Radians

Example Question #26 :Radians

Example Question #27 :Radians

Example Question #28 :Radians

Example Question #29 :Radians

Example Question #30 :Radians

All New SAT Math - Calculator Resources

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