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Trigonometry : Unit Circle and Radians

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Example Questions

Example Question #32 : Radians

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

Possible Answers:

$100^{\circ}$

$248^{\circ}$

$240^{\circ}$

$200^{\circ}$

$250^{\circ}$

Correct answer:

$240^{\circ}$

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, $360^\circ=2\pi \Rightarrow 180^\circ=\pi$ .

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

$\frac{4\pi}{3}*\frac{180}{\pi}=240^{\circ}$ .

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Example Question #51 : Unit Circle And Radians

Convert $\frac{9\pi}{5}$ into degrees.

Possible Answers:

$159^{\circ}$

$355^{\circ}$

$333^{\circ}$

$324^{\circ}$

$300^{\circ}$

Correct answer:

$324^{\circ}$

Explanation:

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

$\frac{9\pi}{5}*\frac{180}{\pi}=324^{\circ}$ .

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Example Question #52 : Unit Circle And Radians

Convert $-\frac{\pi}{3}$ into degrees.

Possible Answers:

$-90^{\circ}$

$-60^{\circ}$

$180^{\circ}$

$-30^{\circ}$

$60^{\circ}$

Correct answer:

$-60^{\circ}$

Explanation:

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

$-\frac{\pi}{3}*\frac{180}{\pi}=-60^{\circ}$ .

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Example Question #41 : Radians

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 #53 : Unit Circle And Radians

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

Possible Answers:

$240^\circ$

$270^\circ$

$250^\circ$

$225^\circ$

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 #51 : Unit Circle And Radians

Round your answer to the nearest thousandth.

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

Possible Answers:

336.151

1.868

$1.868\pi$

1.87

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 #55 : Unit Circle And Radians

Simplify your answer.

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

Possible Answers:

$\frac{\pi }{2}$

$\frac{\pi }{8}$

$\frac{1}{2}$

$\frac{1 }{4}$

$\frac{\pi }{4}$

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 #53 : Unit Circle And Radians

Simplify your answer.

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

Possible Answers:

$120^{\circ}$

$300^{\circ}$

$210^{\circ}$

$150^{\circ}$

120

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 #52 : Unit Circle And Radians

Round your answer to the nearest thousandth.

Convert 3 radians to degrees:

Possible Answers:

$343.775^{\circ}$

$171.887^{\circ}$

$.052^{\circ}$

$60\pi$

$85.944^{\circ}$

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 #53 : Unit Circle And Radians

What is the value in degrees of the following?

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

Possible Answers:

$\theta=400\degree$

$\theta=960\degree$

$\theta=800\degree$

$\theta=936\degree$

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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Trigonometry : Unit Circle and Radians

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #32 : Radians

Example Question #51 : Unit Circle And Radians

Example Question #52 : Unit Circle And Radians

Example Question #41 : Radians

Example Question #53 : Unit Circle And Radians

Example Question #51 : Unit Circle And Radians

Example Question #55 : Unit Circle And Radians

Example Question #53 : Unit Circle And Radians

Example Question #52 : Unit Circle And Radians

Example Question #53 : Unit Circle And Radians

All Trigonometry Resources

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