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New SAT Math - Calculator : New SAT

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2 Diagnostic Tests 27 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #3 : Radians And Conversions

Give $\displaystyle x$ in degrees:

$\frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}$ $\displaystyle \frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}$

Possible Answers:

$x=60^{\circ}$ $\displaystyle x=60^{\circ}$

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

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

$x=36^{\circ}$ $\displaystyle x=36^{\circ}$

$x=40^{\circ}$ $\displaystyle x=40^{\circ}$

Correct answer:

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

Explanation:

First we can find $\displaystyle x$ in radians:

$\frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}\Rightarrow 2(\frac{\pi}{2}-x)=1(\frac{\pi}{2}+x)$ $\displaystyle \frac{\frac{\pi}{2}-x}{\frac{\pi}{2}+x}=\frac{1}{2}\Rightarrow 2(\frac{\pi}{2}-x)=1(\frac{\pi}{2}+x)$

$\Rightarrow \pi-2x=\frac{\pi}{2}+x\Rightarrow \pi-\frac{\pi}{2}=3x$ $\displaystyle \Rightarrow \pi-2x=\frac{\pi}{2}+x\Rightarrow \pi-\frac{\pi}{2}=3x$

$\Rightarrow 3x=\frac{\pi}{2}\Rightarrow x=\frac{\pi}{6}$ $\displaystyle \Rightarrow 3x=\frac{\pi}{2}\Rightarrow x=\frac{\pi}{6}$

To change radians to degrees we need to multiply radians by $\frac{180^{\circ}}{\pi}$ $\displaystyle \frac{180^{\circ}}{\pi}$. So we can write:

$x=\frac{\pi}{6}\Rightarrow x=\frac{\pi}{6}\times \frac{180^{\circ}}{\pi}=30^{\circ}$ $\displaystyle x=\frac{\pi}{6}\Rightarrow x=\frac{\pi}{6}\times \frac{180^{\circ}}{\pi}=30^{\circ}$

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Example Question #3 : Radians

Convert the angle $\frac{7\pi }{3}$ $\displaystyle \frac{7\pi }{3}$ into degrees.

Possible Answers:

$420^{\circ}$ $\displaystyle 420^{\circ}$

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

$840^{\circ}$ $\displaystyle 840^{\circ}$

$500^{\circ}$ $\displaystyle 500^{\circ}$

$210^{\circ}$ $\displaystyle 210^{\circ}$

Correct answer:

$420^{\circ}$ $\displaystyle 420^{\circ}$

Explanation:

To convert radians to degrees, use the conversion $\frac{180^{\circ}}{\pi }$ $\displaystyle \frac{180^{\circ}}{\pi }$.

In this case:

$(\frac{7\pi }{3})*(\frac{180^{\circ}}{\pi }) = 420^{\circ}$ $\displaystyle (\frac{7\pi }{3})*(\frac{180^{\circ}}{\pi }) = 420^{\circ}$

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Example Question #21 : Unit Circle And Radians

How many radians are in $300^\circ$ $\displaystyle 300^\circ$?

Possible Answers:

$\frac{5\pi}{3}$ $\displaystyle \frac{5\pi}{3}$

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

$\frac{3\pi}{5}$ $\displaystyle \frac{3\pi}{5}$

$\pi\sqrt{3}$ $\displaystyle \pi\sqrt{3}$

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

Correct answer:

$\frac{5\pi}{3}$ $\displaystyle \frac{5\pi}{3}$

Explanation:

Since $180^\circ=\pi\ \text{radians}$ $\displaystyle 180^\circ=\pi\ \text{radians}$, we can solve by setting up a proportion:

$\frac{300^\circ}{x}=\frac{180^\circ}{\pi}$ $\displaystyle \frac{300^\circ}{x}=\frac{180^\circ}{\pi}$

Cross-multiply and solve.

$300^\circ*\pi=180^\circ*x$ $\displaystyle 300^\circ*\pi=180^\circ*x$

$\frac{300^\circ}{180^\circ}\pi=x$ $\displaystyle \frac{300^\circ}{180^\circ}\pi=x$

$\frac{5\pi}{3}=x$ $\displaystyle \frac{5\pi}{3}=x$

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Example Question #4 : Circles

How many degrees are in $\frac{5\pi}{6}$ $\displaystyle \frac{5\pi}{6}$ radians?

Possible Answers:

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

$150^\circ$ $\displaystyle 150^\circ$

$210^\circ$ $\displaystyle 210^\circ$

$130^\circ$ $\displaystyle 130^\circ$

$160^\circ$ $\displaystyle 160^\circ$

Correct answer:

$150^\circ$ $\displaystyle 150^\circ$

Explanation:

Since $180^\circ=\pi\ \text{radians}$ $\displaystyle 180^\circ=\pi\ \text{radians}$, we can solve by setting up a proportion:

$\frac{x}{\frac{5\pi}{6}}=\frac{180^\circ}{\pi}$ $\displaystyle \frac{x}{\frac{5\pi}{6}}=\frac{180^\circ}{\pi}$

Cross multiply and solve.

$180^\circ*\frac{5\pi}{6}=x*\pi$ $\displaystyle 180^\circ*\frac{5\pi}{6}=x*\pi$

$\frac{900\pi}{6}=x*\pi$ $\displaystyle \frac{900\pi}{6}=x*\pi$

$150\pi=x*\pi$ $\displaystyle 150\pi=x*\pi$

$\frac{150\pi}{\pi}=x$ $\displaystyle \frac{150\pi}{\pi}=x$

$150^\circ=x$ $\displaystyle 150^\circ=x$

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Example Question #571 : New Sat

Change $\frac{\pi}{5}$ $\displaystyle \frac{\pi}{5}$ angle to degrees.

Possible Answers:

$34^{\circ}$ $\displaystyle 34^{\circ}$

$32^{\circ}$ $\displaystyle 32^{\circ}$

$45^{\circ}$ $\displaystyle 45^{\circ}$

$36^{\circ}$ $\displaystyle 36^{\circ}$

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

Correct answer:

$36^{\circ}$ $\displaystyle 36^{\circ}$

Explanation:

In order to change radians to degrees, we need to multiply the radian agle measure by $\frac{180^{\circ}}{\pi}$ $\displaystyle \frac{180^{\circ}}{\pi}$.

$\frac{\pi}{5}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{5}=36^{\circ}$ $\displaystyle \frac{\pi}{5}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{5}=36^{\circ}$

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Example Question #12 : Radians

An angle of 40 radians is equal to how many degrees?

Possible Answers:

$\frac{3600^{\circ}}{\pi}$ $\displaystyle \frac{3600^{\circ}}{\pi}$

$\frac{5400^{\circ}}{\pi}$ $\displaystyle \frac{5400^{\circ}}{\pi}$

$\frac{720^{\circ}}{\pi}$ $\displaystyle \frac{720^{\circ}}{\pi}$

$\frac{7200^{\circ}}{\pi}$ $\displaystyle \frac{7200^{\circ}}{\pi}$

$\frac{7000^{\circ}}{\pi}$ $\displaystyle \frac{7000^{\circ}}{\pi}$

Correct answer:

$\frac{7200^{\circ}}{\pi}$ $\displaystyle \frac{7200^{\circ}}{\pi}$

Explanation:

We know that one radian is equal to $\frac{180^{\circ}}{\pi}$ $\displaystyle \frac{180^{\circ}}{\pi}$, so in order to change $\displaystyle 40$ radians to degrees we need to multiply $\displaystyle 40$ by $\frac{180^{\circ}}{\pi}$ $\displaystyle \frac{180^{\circ}}{\pi}$.

$40\times \frac{180^{\circ}}{\pi}=\frac{7200^{\circ}}{\pi}$ $\displaystyle 40\times \frac{180^{\circ}}{\pi}=\frac{7200^{\circ}}{\pi}$

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Example Question #572 : New Sat

Change $\frac{17\pi}{5}$ $\displaystyle \frac{17\pi}{5}$ angle to degrees.

Possible Answers:

$412^{\circ}$ $\displaystyle 412^{\circ}$

$512^{\circ}$ $\displaystyle 512^{\circ}$

$620^{\circ}$ $\displaystyle 620^{\circ}$

$612^{\circ}$ $\displaystyle 612^{\circ}$

$712^{\circ}$ $\displaystyle 712^{\circ}$

Correct answer:

$612^{\circ}$ $\displaystyle 612^{\circ}$

Explanation:

In order to change radians to degrees we need to multiply the radians by $\frac{180^{\circ}}{\pi}$ $\displaystyle \frac{180^{\circ}}{\pi}$.

$\frac{17\pi}{5}\times \frac{180^{\circ}}{\pi}=\frac{17\times 180^{\circ}}{5}=612^{\circ}$ $\displaystyle \frac{17\pi}{5}\times \frac{180^{\circ}}{\pi}=\frac{17\times 180^{\circ}}{5}=612^{\circ}$

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Example Question #573 : New Sat

Change $75^{\circ}$ $\displaystyle 75^{\circ}$ to radians.

Possible Answers:

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

$\frac{\pi}{12}$ $\displaystyle \frac{\pi}{12}$

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

$\frac{7\pi}{12}$ $\displaystyle \frac{7\pi}{12}$

$\frac{5\pi}{12}$ $\displaystyle \frac{5\pi}{12}$

Correct answer:

$\frac{5\pi}{12}$ $\displaystyle \frac{5\pi}{12}$

Explanation:

In order to change degrees to radians we need to multiply the degrees by $\frac{\pi}{180^{\circ}}$ $\displaystyle \frac{\pi}{180^{\circ}}$.

$75^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{5\pi}{12}$ $\displaystyle 75^{\circ}\times \frac{\pi}{180^{\circ}}=\frac{5\pi}{12}$

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Example Question #24 : Unit Circle And Radians

Change the following expression to degrees:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}$ $\displaystyle \frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}$

Possible Answers:

$75^{\circ}$ $\displaystyle 75^{\circ}$

$120^{\circ}$ $\displaystyle 120^{\circ}$

$160^{\circ}$ $\displaystyle 160^{\circ}$

$60^{\circ}$ $\displaystyle 60^{\circ}$

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

Correct answer:

$60^{\circ}$ $\displaystyle 60^{\circ}$

Explanation:

First we need to simplify the expression:

$\frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}=\frac{\frac{2\pi-\pi}{6}}{\frac{2+1}{6}}=\frac{\pi}{3}$ $\displaystyle \frac{\frac{\pi}{3}-\frac{\pi}{6}}{\frac{1}{3}+\frac{1}{6}}=\frac{\frac{2\pi-\pi}{6}}{\frac{2+1}{6}}=\frac{\pi}{3}$

Now multiply by $\frac{180^{\circ}}{\pi}$ $\displaystyle \frac{180^{\circ}}{\pi}$:

$\frac{\pi}{3}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{3}=60^{\circ}$ $\displaystyle \frac{\pi}{3}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{3}=60^{\circ}$

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Example Question #25 : Unit Circle And Radians

Change the following expression to degrees:

${\frac{\pi}{4}-\frac{\pi}{12}}$ $\displaystyle {\frac{\pi}{4}-\frac{\pi}{12}}$

Possible Answers:

$75^{\circ}$ $\displaystyle 75^{\circ}$

$60^{\circ}$ $\displaystyle 60^{\circ}$

$45^{\circ}$ $\displaystyle 45^{\circ}$

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

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

Correct answer:

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

Explanation:

First we need to simplify the expression:

${\frac{\pi}{4}-\frac{\pi}{12}}=\frac{3\pi-\pi}{12}=\frac{2\pi}{12}=\frac{\pi}{6}$ $\displaystyle {\frac{\pi}{4}-\frac{\pi}{12}}=\frac{3\pi-\pi}{12}=\frac{2\pi}{12}=\frac{\pi}{6}$

Then multiply the radians by $\frac{180^{\circ}}{\pi}$ $\displaystyle \frac{180^{\circ}}{\pi}$:

$\frac{\pi}{6}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{6}=30^{\circ}$ $\displaystyle \frac{\pi}{6}\times \frac{180^{\circ}}{\pi}=\frac{180^{\circ}}{6}=30^{\circ}$

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New SAT Math - Calculator : New SAT

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

All New SAT Math - Calculator Resources

Example Questions

Example Question #3 : Radians And Conversions

Example Question #3 : Radians

Example Question #21 : Unit Circle And Radians

Example Question #4 : Circles

Example Question #571 : New Sat

Example Question #12 : Radians

Example Question #572 : New Sat

Example Question #573 : New Sat

Example Question #24 : Unit Circle And Radians

Example Question #25 : Unit Circle And Radians

All New SAT Math - Calculator Resources

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