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High School Math : High School Math

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8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : The Unit Circle And Radians

What is $\sin(\frac{3\pi}{4})$ $\displaystyle \sin(\frac{3\pi}{4})$ ?

Possible Answers:

$\displaystyle 1$

$\frac{\sqrt{2}}{2}$ $\displaystyle \frac{\sqrt{2}}{2}$

$\displaystyle -1$

$\frac{-\sqrt2}{2}$ $\displaystyle \frac{-\sqrt2}{2}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\frac{\sqrt{2}}{2}$ $\displaystyle \frac{\sqrt{2}}{2}$

Explanation:

Using the unit circle, $\sin(\frac{3\pi}{4})=\frac{\sqrt2}{2 }$ $\displaystyle \sin(\frac{3\pi}{4})=\frac{\sqrt2}{2 }$ . You can also think of this as the sine of $135^\circ$ $\displaystyle 135^\circ$ , which would also be $\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$ .

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Example Question #1 : Using The Unit Circle

What is $\cos (\frac{3\pi}{4})$ $\displaystyle \cos (\frac{3\pi}{4})$ ?

Possible Answers:

$-\frac{\sqrt2}{2}$ $\displaystyle -\frac{\sqrt2}{2}$

$\frac{2\sqrt2}{2}$ $\displaystyle \frac{2\sqrt2}{2}$

$\displaystyle -1$

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

$\displaystyle 1$

Correct answer:

$-\frac{\sqrt2}{2}$ $\displaystyle -\frac{\sqrt2}{2}$

Explanation:

Using the unit circle, you can see that the $\cos (\frac{3\pi}{4})=-\frac{\sqrt2}{2}$ $\displaystyle \cos (\frac{3\pi}{4})=-\frac{\sqrt2}{2}$ . Since the angle is in Qudrant II, sine is positive and cosine is negative.

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Example Question #2 : The Unit Circle And Radians

What is $\sin(\frac{\pi}{4})$ $\displaystyle \sin(\frac{\pi}{4})$ ?

Possible Answers:

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 1$

$-\frac{\sqrt2}{2}$ $\displaystyle -\frac{\sqrt2}{2}$

$\displaystyle -1$

Correct answer:

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

Explanation:

Using the unit circle, $\sin(\frac{\pi}{4})=\frac{\sqrt2}{2 }$ $\displaystyle \sin(\frac{\pi}{4})=\frac{\sqrt2}{2 }$ . You can also think of this as the sine of $45^\circ$ $\displaystyle 45^\circ$ , which would also be $\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$ .

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Example Question #21 : Graphing The Sine And Cosine Functions

What is $\sin(\pi)$ $\displaystyle \sin(\pi)$ ?

Possible Answers:

$\frac{\sqrt{2}}{2}$ $\displaystyle \frac{\sqrt{2}}{2}$

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

$\displaystyle 0$

$\displaystyle 1$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\displaystyle 0$

Explanation:

If you examine the unit circle, you'll see that that $\sin(\pi)=0$ $\displaystyle \sin(\pi)=0$ .

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Example Question #22 : Graphing The Sine And Cosine Functions

What is $\cos(\pi)$ $\displaystyle \cos(\pi)$ ?

Possible Answers:

$\displaystyle 1$

$\displaystyle 0$

$\frac{\sqrt3}{2}$ $\displaystyle \frac{\sqrt3}{2}$

$\displaystyle -1$

$\frac{\sqrt2}{2}$ $\displaystyle \frac{\sqrt2}{2}$

Correct answer:

$\displaystyle -1$

Explanation:

If you examine the unit circle, you'll see that the value of $\cos(\pi)=-1$ $\displaystyle \cos(\pi)=-1$ . You can also get this by examining a cosine graph and you'll see it crosses the point $(\pi,-1)$ $\displaystyle (\pi,-1)$ .

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Example Question #1 : Understanding Radians And Conversions

What is the value of the angle $\frac{3\pi}{2}$ $\displaystyle \frac{3\pi}{2}$ radians when converted to degrees?

Possible Answers:

270 $\displaystyle 270$

$\displaystyle -180$

$\displaystyle 90$

$\displaystyle -45$

135 $\displaystyle 135$

Correct answer:

270 $\displaystyle 270$

Explanation:

The answer can be found using the conversion of 1 radian equals $\frac{180}{\pi}$ $\displaystyle \frac{180}{\pi}$ degrees. Multiplying $\frac{3\pi}{2}$ $\displaystyle \frac{3\pi}{2}$ by this conversion factor gives 270 degrees.

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Example Question #11 : The Unit Circle And Radians

A point has Cartesian coordinates (1,3) $\displaystyle (1,3)$ . Rewrite this as an ordered pair in the polar coordinate plane, rounding the coordinates to the nearest hundredth.

Possible Answers:

$\displaystyle (2.83, 0.32)$

$\displaystyle (3.16,0.32)$

$\displaystyle (3.16,0.80)$

$\displaystyle (2.83, 1.25)$

$\displaystyle (3.16,1.25)$

Correct answer:

$\displaystyle (3.16,1.25)$

Explanation:

Set $\displaystyle x=1, y=3$ . Calculate the polar coordinates $(r,\theta )$ $\displaystyle (r,\theta )$ as follows:

$r = \sqrt{x^{2}+y^{2}}= \sqrt{1^{2}+3^{2}}=\sqrt{10} \approx 3.16$ $\displaystyle r = \sqrt{x^{2}+y^{2}}= \sqrt{1^{2}+3^{2}}=\sqrt{10} \approx 3.16$

$\theta = \arctan \frac{y}{x}= \arctan \frac{3}{1} = \arctan 3 \approx 1.25$ $\displaystyle \theta = \arctan \frac{y}{x}= \arctan \frac{3}{1} = \arctan 3 \approx 1.25$

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Example Question #34 : Trigonometry

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

Possible Answers:

$45^\circ$ $\displaystyle 45^\circ$

$120^\circ$ $\displaystyle 120^\circ$

$360^\circ$ $\displaystyle 360^\circ$

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

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

Correct answer:

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

Explanation:

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

Cross multiply:

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

Notice that the $\pi$ $\displaystyle \pi$ 's cancel out:

$x^\circ=180^\circ*\frac{1}{6}$ $\displaystyle x^\circ=180^\circ*\frac{1}{6}$

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

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Example Question #2 : Understanding Radians And Conversions

How many radians are in $180^\circ$ $\displaystyle 180^\circ$ ?

Possible Answers:

$4\pi$ $\displaystyle 4\pi$

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

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

$\pi$ $\displaystyle \pi$

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

Correct answer:

$\pi$ $\displaystyle \pi$

Explanation:

The relationship between degrees and radians is $180^\circ=\pi$ $\displaystyle 180^\circ=\pi$ radians. Therefore, $180^\circ$ $\displaystyle 180^\circ$ would be $\pi$ $\displaystyle \pi$ radians.

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Example Question #3 : Understanding Radians And Conversions

Express in radians: $125^{\circ }$ $\displaystyle 125^{\circ }$

Possible Answers:

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

$\frac{11\pi }{18}$ $\displaystyle \frac{11\pi }{18}$

$\frac{15\pi }{36}$ $\displaystyle \frac{15\pi }{36}$

$\frac{25\pi }{36}$ $\displaystyle \frac{25\pi }{36}$

$\frac{5\pi }{9}$ $\displaystyle \frac{5\pi }{9}$

Correct answer:

$\frac{25\pi }{36}$ $\displaystyle \frac{25\pi }{36}$

Explanation:

Since $180 ^{\circ } = \pi \textrm{ rad}$ $\displaystyle 180 ^{\circ } = \pi \textrm{ rad}$ , we can convert as follows:

$125 \cdot \frac{\pi }{180} = \frac{25\pi }{36}$ $\displaystyle 125 \cdot \frac{\pi }{180} = \frac{25\pi }{36}$

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All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #4 : The Unit Circle And Radians

Example Question #1 : Using The Unit Circle

Example Question #2 : The Unit Circle And Radians

Example Question #21 : Graphing The Sine And Cosine Functions

Example Question #22 : Graphing The Sine And Cosine Functions

Example Question #1 : Understanding Radians And Conversions

Example Question #11 : The Unit Circle And Radians

Example Question #34 : Trigonometry

Example Question #2 : Understanding Radians And Conversions

Example Question #3 : Understanding Radians And Conversions

All High School Math Resources

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