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New SAT Math - Calculator : Circles

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Example Questions

Example Question #431 : Trigonometry

Convert $75^\circ$ into radians

Possible Answers:

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

$\frac {5\pi}{18}$

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

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

Correct answer:

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

Explanation:

Step 1: Recall the formula to change a degree measure into radians:

The formula is: $Degree\cdot \frac {\pi}{180}$ .

Step 2: Plug in the angle:

$75 \cdot \frac {\pi}{180}$

Step 3: Simplify:

We will use the and try to reduce the 180 as much as possible.

After Dividing by 3:

$25 \cdot \frac {\pi}{60}$

After dividing by 5:

$5 \cdot \frac {\pi}{12}=\frac {5\pi}{12}$

$75^\circ$ is $\frac {5\pi}{12}$ in radians.

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Example Question #601 : New Sat

Convert $\frac {4\pi}{3}$ in degrees.

Possible Answers:

$225^\circ$

$270^\circ$

$240^\circ$

$250^\circ$

Correct answer:

$240^\circ$

Explanation:

Step 1: To convert radians back to degrees, multiply that radian measure by $\frac {180}{\pi}$

Step 2: Multiply:

$\frac {4\pi}{3}\cdot \frac {180}{\pi}$

Step 3: Reduce.. The $\pi$ will cancel...

$\frac {4}{3} \cdot 180$

Step 4: Divide 180 by ..

$4\cdot 60^\circ=240^\circ$

$\frac {4\pi}{3}$ is equivalent to $240^\circ$

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Example Question #41 : Circles

Round your answer to the nearest thousandth.

Convert $107^{\circ}$ to radians:

Possible Answers:

1.87

1.868

$1.868\pi$

336.151

Correct answer:

1.868

Explanation:

We know that:

$360^{\circ}=2\pi$ Radians

since the giving angle was in degrees then we multiply

$107^{\circ}*\frac{\pi}{180^{\circ}}= 1.868$

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Example Question #603 : New Sat

Simplify your answer.

Convert $45^{\circ}$ to radians:

Possible Answers:

$\frac{1 }{4}$

$\frac{\pi }{2}$

$\frac{1}{2}$

$\frac{\pi }{4}$

$\frac{\pi }{8}$

Correct answer:

$\frac{\pi }{4}$

Explanation:

We know that:

$360^{\circ}=2\pi$ Radians

since the giving angle was in degrees then we multiply

$45^{\circ}*\frac{\pi}{180^{\circ}}= \frac{\pi}{4}$

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Example Question #44 : Radians And Conversions

Simplify your answer.

Convert $\frac{5\pi}{6}$ to degree:

Possible Answers:

$120^{\circ}$

120

$210^{\circ}$

$150^{\circ}$

$300^{\circ}$

Correct answer:

$150^{\circ}$

Explanation:

We know that:

$360^{\circ}=2\pi$ Radians

since the giving angle was in radians then we multiply

$\frac{5\pi}{6}*\frac{180}{\pi}= 150^{\circ}$

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Example Question #42 : Circles

Round your answer to the nearest thousandth.

Convert 3 radians to degrees:

Possible Answers:

$343.775^{\circ}$

$.052^{\circ}$

$60\pi$

$85.944^{\circ}$

$171.887^{\circ}$

Correct answer:

$171.887^{\circ}$

Explanation:

We know that:

$360^{\circ}=2\pi$ Radians

since the giving angle was in radians then we multiply

$3*\frac{180}{\pi}= 171.887^{\circ}$

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Example Question #43 : Circles

What is the value in degrees of the following?

$\theta=\frac{26\pi}{5}$

Possible Answers:

$\theta=400\degree$

$\theta=936\degree$

$\theta=800\degree$

$\theta=960\degree$

Correct answer:

$\theta=936\degree$

Explanation:

To convert from radians to degrees, you must multiply by $\frac{180\degree}{\pi}$ .

The pi units will cancel out, leaving you with degrees.

Plugging into a calculator, you obtain

$\frac{26\pi}{5}\cdot \frac{180\degree}{\pi}$

$\theta=936\degree$ .

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Example Question #61 : Unit Circle And Radians

Convert $\frac{11\pi}{5}$ into degrees.

Possible Answers:

$300\degree$

$400\degree$

$395\degree$

$396\degree$

Correct answer:

$396\degree$

Explanation:

To convert from radians to degrees, you must multiply the angle by $\frac{180\degree}{\pi}$ to cancel the $\pi$ units.

This will get you

$11\cdot \frac{180\degree}{5}=396^\circ$

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Example Question #611 : New Sat

Convert $\frac{2\pi}{5}$ to degrees:

Possible Answers:

$72\pi$

$72^{\circ}$

$114^{\circ}$

$36^{\circ}$

$\frac{2}{5}^{\circ}$

Correct answer:

$72^{\circ}$

Explanation:

To convert radians to degrees, we need to multiply the given radians by $\frac{180^{\circ}}{\pi}$ .

$\frac{2\pi}{5}*\frac{180^{\circ}}{\pi}=\frac{360^{\circ}}{5}=72^{\circ}$

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Example Question #49 : Radians And Conversions

Give your answer in terms of $\pi$ .

Convert $165^{\circ}$ to radians:

Possible Answers:

$\frac{12\pi}{11}$

$\frac{\pi}{12}$

$\frac{11\pi}{12}$

$\frac{11\pi}{24}$

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

Correct answer:

$\frac{11\pi}{12}$

Explanation:

To convert degrees to radians, we need to multiply the given degree by $\frac{\pi}{180^{\circ}}$ .

$165*^{\circ}\frac{\pi}{180^{\circ}}=\frac{165\pi}{180}$

To simplify, we get:

$\frac{11\pi}{12}$

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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 #431 : Trigonometry

Example Question #601 : New Sat

Example Question #41 : Circles

Example Question #603 : New Sat

Example Question #44 : Radians And Conversions

Example Question #42 : Circles

Example Question #43 : Circles

Example Question #61 : Unit Circle And Radians

Example Question #611 : New Sat

Example Question #49 : Radians And Conversions

All New SAT Math - Calculator Resources

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