New SAT Reading : New SAT

Study concepts, example questions & explanations for New SAT Reading

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Example Questions

Example Question #191 : New Sat Math Calculator

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

Possible Answers:

\displaystyle 345^{\circ}

\displaystyle 225^{\circ}

\displaystyle 270^{\circ}

\displaystyle 315^{\circ}

\displaystyle 285^{\circ}

Correct answer:

\displaystyle 315^{\circ}

Explanation:

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

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

The quantity of radians given in the problem is \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 \displaystyle \Theta and set up a proportion equation using the aforementioned definition relating radians to degrees:

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

Cross-multiply the denominators in these fractions to obtain:

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

or

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

Canceling like terms in these equations yields

\displaystyle \Theta = 315^{\circ}

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

Example Question #591 : New Sat

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

Possible Answers:

\displaystyle 350^\circ

\displaystyle 370^\circ

\displaystyle 185^\circ

\displaystyle 10^\circ

Correct answer:

\displaystyle 370^\circ

Explanation:

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

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

Example Question #22 : Radians

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

Possible Answers:

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

\displaystyle \frac{\pi}{6}

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

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

\displaystyle \frac{\pi}{4}

Correct answer:

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

Explanation:

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

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

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

So in this particular case, 

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

Example Question #23 : Radians

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

Possible Answers:

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

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

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

\displaystyle \frac{\pi}{3}

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

Correct answer:

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

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

So in this particular case,

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

Example Question #591 : New Sat

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

Possible Answers:

\displaystyle \frac{\pi}{180}

\displaystyle \frac{\pi}{360}

\displaystyle \pi

\displaystyle \frac{\pi}{90}

\displaystyle 2\pi

Correct answer:

\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,

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

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

So in this particular case, 

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

Example Question #31 : Radians

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

Possible Answers:

\displaystyle \frac{\pi}{360}

\displaystyle \frac{\pi}{180}

\displaystyle \frac{\pi}{90}

\displaystyle 2\pi

\displaystyle \pi

Correct answer:

\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,

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

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

So in this particular case, 

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

Example Question #201 : New Sat Math Calculator

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

Possible Answers:

\displaystyle \frac{\pi}{90}

\displaystyle \frac{\pi}{36}

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

\displaystyle \frac{\pi}{18}

\displaystyle \frac{\pi}{180}

Correct answer:

\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,

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

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

So in this particular case, 

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

Example Question #201 : New Sat Math Calculator

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

Possible Answers:

\displaystyle \frac{\pi}{5}

\displaystyle 3\pi

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

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

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

Correct answer:

\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,

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

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

So in this particular case, 

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

Example Question #32 : Circles

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

Possible Answers:

\displaystyle 55^\circ

\displaystyle 60^\circ

\displaystyle 90^\circ

\displaystyle 180^\circ

\displaystyle 30^\circ

Correct answer:

\displaystyle 90^\circ

Explanation:

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

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

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

So, 

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

Example Question #202 : New Sat Math Calculator

Convert \displaystyle \pi into degrees.

Possible Answers:

\displaystyle 3.14^{\circ}

\displaystyle 30^{\circ}

\displaystyle 90^{\circ}

\displaystyle 360^{\circ}

\displaystyle 180^{\circ}

Correct answer:

\displaystyle 180^{\circ}

Explanation:

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

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

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

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

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