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New SAT Writing and Language : New SAT

Study concepts, example questions & explanations for New SAT Writing and Language

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All New SAT Writing and Language Resources

3 Diagnostic Tests 39 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #611 : New Sat

What is the value in degrees of the following?

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

Possible Answers:

$\theta=400\degree$

$\theta=800\degree$

$\theta=960\degree$

$\theta=936\degree$

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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Example Question #612 : New Sat

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

Possible Answers:

$300\degree$

$395\degree$

$396\degree$

$400\degree$

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 #613 : New Sat

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

Possible Answers:

$36^{\circ}$

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

$72\pi$

$72^{\circ}$

$114^{\circ}$

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 #44 : Circles

Give your answer in terms of $\pi$ .

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

Possible Answers:

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

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

$\frac{\pi}{12}$

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

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

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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Example Question #63 : Unit Circle And Radians

Convert $52^{\circ}$ to radians.

Possible Answers:

$\frac{\pi}{2}$

$\frac{\pi}{5}$

$\tfrac{17}{12}\pi$

$\tfrac{13}{45}\pi$

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

Correct answer:

$\tfrac{13}{45}\pi$

Explanation:

To convert between degrees and radians, multiply by $\frac{\pi }{180^{\circ}}$ or $\frac{180^{\circ}}{\pi}$ .

Since we start in degrees, we use $\frac{\pi }{180^{\circ}}$ :

$\frac{52^{\circ}}{1}\times\frac{\pi}{180^{\circ}}=\frac{52}{180}\pi$

which simplifies to $\tfrac{13}{45}\pi$ .

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Example Question #1 : Sin, Cos, Tan

Find the value of the trigonometric function in fraction form for triangle ABC .

Triangle

What is the cosine of $\angle B$ ?

Possible Answers:

24/25

7/24

$\frac{7}{25}$

Correct answer:

$\frac{7}{25}$

Explanation:

The cosine of an angle is the value of the adjacent side over the hypotenuse.

Therefore:

$cos \angle B = \frac{adjacent}{hypotenuse} = \frac{7}{25}$

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Example Question #1 : Sine, Cosine, & Tangent

If cos x = 0.2 $\small \cosx$ and sin x = 0.4, what is the value of tan x?

Possible Answers:

0.035

Correct answer:

Explanation:

$\small \tan{x}=\frac{\sin{x}}{\cos{x}}$

$\small \small \tan{x}=\frac{0.4}{0.2}$

$\small \tan{x}=0.035$

$\small x=\tan^{-1}0.035$

$\small x=2$

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Example Question #1 : Sin, Cos, Tan

What is the value of sin(30)+sin(60) ?

Possible Answers:

$\frac{\sqrt3+1}{2}$

$\frac{\sqrt3-1}{2}$

Correct answer:

$\frac{\sqrt3+1}{2}$

Explanation:

Solve each term separately.

$cos(30)= \frac{\sqrt3}{2}$

$cos(60)=\frac{1}{2}$

Add both terms.

$\frac{\sqrt3}{2}+\frac{1}{2}= \frac{\sqrt3+1}{2}$

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Example Question #1 : Sin, Cos, Tan

Determine the value of 2tan(120) .

Possible Answers:

$\sqrt3$

$-\sqrt3$

$-\frac{\sqrt3}{2}$

$-2\sqrt3$

$2\sqrt3$

Correct answer:

$-2\sqrt3$

Explanation:

Rewrite 2tan(120) in terms of sines and cosines.

$2tan(120)=2(\frac{sin(120)}{cos(120)})=2(\frac{\frac{\sqrt3}{2}}{-\frac{1}{2}})$

Simplify the complex fraction.

$2(\frac{\frac{\sqrt3}{2}}{-\frac{1}{2}})= 2\times\frac{\sqrt3}{2}\times-2 = -2\sqrt3$

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Example Question #2 : Sin, Cos, Tan

Find the value of $\frac{1}{2}sin(45)+ tan(60)$ .

Possible Answers:

$\frac{3\sqrt2+\sqrt3}{12}$

$\frac{\sqrt2-4\sqrt3}{2}$

$\sqrt2+\sqrt3$

$\frac{\sqrt2+4\sqrt3}{2}$

$\frac{\sqrt2+4\sqrt3}{4}$

Correct answer:

$\frac{\sqrt2+4\sqrt3}{4}$

Explanation:

To find the value of $\frac{1}{2}sin(45)+ tan(60)$ , solve each term separately.

$\frac{1}{2}sin(45)=\frac{1}{2} \cdot \frac{\sqrt2}{2} = \frac{\sqrt2}{4}$

$tan(60) = \sqrt3$

Sum the two terms.

$\frac{\sqrt2}{4}+\sqrt3 = \frac{\sqrt2}{4}+\frac{4\sqrt3}{4} = \frac{\sqrt2+4\sqrt3}{4}$

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New SAT Writing and Language : New SAT

Study concepts, example questions & explanations for New SAT Writing and Language

All New SAT Writing and Language Resources

Example Questions

Example Question #611 : New Sat

Example Question #612 : New Sat

Example Question #613 : New Sat

Example Question #44 : Circles

Example Question #63 : Unit Circle And Radians

Example Question #1 : Sin, Cos, Tan

Example Question #1 : Sine, Cosine, & Tangent

Example Question #1 : Sin, Cos, Tan

Example Question #1 : Sin, Cos, Tan

Example Question #2 : Sin, Cos, Tan

All New SAT Writing and Language Resources

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