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New SAT Math - Calculator : New SAT Math - Calculator

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All New SAT Math - Calculator Resources

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

Example Questions

Example Question #43 : Circles

Give your answer in terms of $\pi$ .

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

Possible Answers:

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

$\frac{\pi}{12}$

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

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

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

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 #613 : New Sat

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

Possible Answers:

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

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

$\frac{\pi}{5}$

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

$\frac{\pi}{2}$

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

$\frac{7}{25}$

7/24

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 #221 : New Sat Math Calculator

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 #2 : Sine, Cosine, & Tangent

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:

$2\sqrt3$

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

$-\sqrt3$

$\sqrt3$

$-2\sqrt3$

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 #1 : Sine, Cosine, & Tangent

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

Possible Answers:

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

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

$\sqrt2+\sqrt3$

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

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

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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Example Question #1 : Sin, Cos, Tan

Select the ratio that would give Tan B.

Possible Answers:

None of the other answers.

$\tan B=\frac{CB}{AC}$

$\tan B=\frac{AC}{AB}$

$\tan B=\frac{CB}{AB}$

$\tan B=\frac{AB}{AC}$

Correct answer:

$\tan B=\frac{AC}{AB}$

Explanation:

We need the Tan B. Which side lengths correspond to this ratio?

$\tan=\frac{opp}{adj}$

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Example Question #2 : Sin, Cos, Tan

Calculate $tan(\frac{4\pi}{3})$ .

Possible Answers:

$\sqrt{3}$

$-\sqrt{3}$

Correct answer:

$\sqrt{3}$

Explanation:

The tangent function has a period of $\pi$ units. That is,

$tan(x+n\pi)=tanx$

for all $n\in\mathbb{Z}$ .

Since $\frac{4\pi}{3}=\frac{\pi}{3}+\pi$ , we can rewrite the original expression $tan(\frac{4\pi}{3})$ as follows:

$tan(\frac{4\pi}{3})=tan(\frac{\pi}{3}+\pi)$

$=tan(\frac{\pi}{3})$

$=\frac{sin(\frac{\pi}{3})}{cos(\frac{\pi}{3})}$

$=\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}$

$=\sqrt{3}$

Hence,

$tan(\frac{4\pi}{3})=\sqrt{3}$

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Example Question #2 : Sine, Cosine, & Tangent

Calculate $cos(\frac{5\pi}{3})$ .

Possible Answers:

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

$\frac{1}{2}$

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

$-\frac{1}{2}$

Correct answer:

$\frac{1}{2}$

Explanation:

First, convert the given angle measure from radians to degrees:

$cos(\frac{5\pi}{3})=cos(300^{\circ})$

Next, recall that $300^{\circ}$ lies in the fourth quadrant of the unit circle, wherein the cosine is positive. Furthermore, the reference angle of $300^{\circ}$ is

$360^{\circ}-300^{\circ}=60^{\circ}$

Hence, all that is required is to recognize from these observations that

$cos(\frac{5\pi}{3})=cos(300^{\circ}) =cos(60^{\circ})$ ,

which is $\frac{1}{2}$ .

Therefore,

$cos(\frac{5\pi}{3})=\frac{1}{2}$

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New SAT Math - Calculator : New SAT Math - Calculator

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

All New SAT Math - Calculator Resources

Example Questions

Example Question #43 : Circles

Example Question #613 : New Sat

Example Question #1 : Sin, Cos, Tan

Example Question #221 : New Sat Math Calculator

Example Question #2 : Sine, Cosine, & Tangent

Example Question #1 : Sin, Cos, Tan

Example Question #1 : Sine, Cosine, & Tangent

Example Question #1 : Sin, Cos, Tan

Example Question #2 : Sin, Cos, Tan

Example Question #2 : Sine, Cosine, & Tangent

All New SAT Math - Calculator Resources

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