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Example Questions

Example Question #441 : Trigonometry

Convert $\frac{7\pi}{4}$ $\displaystyle \frac{7\pi}{4}$ radians into degrees.

Possible Answers:

$270^{\circ}$ $\displaystyle 270^{\circ}$

$345^{\circ}$ $\displaystyle 345^{\circ}$

$225^{\circ}$ $\displaystyle 225^{\circ}$

$315^{\circ}$ $\displaystyle 315^{\circ}$

$285^{\circ}$ $\displaystyle 285^{\circ}$

Correct answer:

$315^{\circ}$ $\displaystyle 315^{\circ}$

Explanation:

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

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

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

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

Cross-multiply the denominators in these fractions to obtain:

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

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

Canceling like terms in these equations yields

$\Theta = 315^{\circ}$ $\displaystyle \Theta = 315^{\circ}$

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

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Example Question #591 : New Sat

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

Possible Answers:

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

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

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

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

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 #24 : Circles

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

Possible Answers:

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

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

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

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

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

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 #25 : Circles

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

Possible Answers:

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

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

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

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

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

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 #201 : New Sat Math Calculator

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

Possible Answers:

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

$\pi$ $\displaystyle \pi$

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

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

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

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 #32 : Radians

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

Possible Answers:

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

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

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

$\pi$ $\displaystyle \pi$

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

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 #33 : Radians

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

Possible Answers:

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

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

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

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

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

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 #31 : Radians

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

Possible Answers:

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

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

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

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

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

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 #35 : Radians

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

Possible Answers:

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

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

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

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

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

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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Example Question #36 : Radians

Convert $\pi$ $\displaystyle \pi$ into degrees.

Possible Answers:

$30^{\circ}$ $\displaystyle 30^{\circ}$

$360^{\circ}$ $\displaystyle 360^{\circ}$

$180^{\circ}$ $\displaystyle 180^{\circ}$

$3.14^{\circ}$ $\displaystyle 3.14^{\circ}$

$90^{\circ}$ $\displaystyle 90^{\circ}$

Correct answer:

$180^{\circ}$ $\displaystyle 180^{\circ}$

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 in this particular case,

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

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New SAT Reading : New SAT

Study concepts, example questions & explanations for New SAT Reading

All New SAT Reading Resources

Example Questions

Example Question #441 : Trigonometry

Example Question #591 : New Sat

Example Question #24 : Circles

Example Question #25 : Circles

Example Question #201 : New Sat Math Calculator

Example Question #32 : Radians

Example Question #33 : Radians

Example Question #31 : Radians

Example Question #35 : Radians

Example Question #36 : Radians

All New SAT Reading Resources

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