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New SAT Math - Calculator : New SAT Math - Calculator

Study concepts, example questions & explanations for 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 #1 : Sin, Cos, Tan

What is the result when the following expression is simplified as much as possible?

$\sin(2h)\sec(h)+2\sin(-h)$

Possible Answers:

$\sec h$

$2\sin h$

Correct answer:

Explanation:

Because $\sin x$ is an odd function, we can rewrite the second term in the expression.

$2\sin(-h)=-2\sin h$ .

We now use a double-angle formula to expand the first term.

$\sin(2h)\sec h=2\sin h\cos h\sec h$ .

Because they are reciprocals, $\cos h\sec h=1$ .

$2\sin h\cos h\sec h-2\sin h=2\sin h-2\sin h=0.$

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Example Question #621 : New Sat

Round to the nearest hundredth.

Use your calculator to find:

$\sin72^{\circ}$

Possible Answers:

0.25

None of the above

0.72

0.95

Correct answer:

0.95

Explanation:

Before plugging the function into the calculator make sure the mode of the calculator is set to degrees,

Plug in $\sin72^{\circ}$ which equals to 0.95 .

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Example Question #1 : Trigonometric Operations

Round to the nearest hundredth.

Use your calculator to find:

$\cos \frac{3\pi}{8}$

Possible Answers:

0.38

None of the above

0.95

Correct answer:

0.38

Explanation:

Before plugging the function into the calculator make sure the mode of the calculator is set to radians,

plug in

$\cos \frac{3\pi}{8}$

which is equal to 0.38 .

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Example Question #11 : Sin, Cos, Tan

What is the value of cos30^o . sin30^o . tan60^o

Possible Answers:

$\small \sqrt{3}$

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

$\small \frac{\sqrt{3}}{4}$

$\small \frac{3}{4}$

$\small \frac{1}{2}$

Correct answer:

$\small \frac{3}{4}$

Explanation:

Solution

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Example Question #11 : Sin, Cos, Tan

$\left ( \sin15 + \cos\15 \right )^{2}$ What is the closest value to this expression?

Possible Answers:

2.5

1.5

Correct answer:

1.5

Explanation:

First you have to know the equation for $\left ( a+b\right )^{2} = a^{2}+2ab+b^{2}$ and apply it to our equation. Second the formula of $\sin^{2}+\cos^{2}=1$ will allow you to get rid of the square sin and cos. Third the equation $\sin2x = 2\sin \cos$ will allow you to get rid of the 2ab . Therefore, we will have a $\sin(30)$ , and that will be equal to 0.5 . Sum and 0.5 and you will get 1.5

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Example Question #11 : Sin, Cos, Tan

if $\cos x = \frac{4}{5}$ What is $\sin2x$ ?

Possible Answers:

$\frac{5}{13}$

$\frac{24}{25}$

$\frac{3}{5}$

$\frac{7}{25}$

$\frac{12}{13}$

Correct answer:

$\frac{7}{25}$

Explanation:

Remember two things. First if $\cos x=\frac{4}{5}$ , find the $\sin(x)$ by using the Pythagoras Theorem. If one side is and the hypotenuse is , then the other side is . $\sin x$ will be $\frac{3}{5}$ . Finally remember the formula for $\sin2x = 2\sin x *\cos x$ . And just place the things we found to the equation.

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Example Question #1 : Plane Geometry

Two angles are supplementary and have a ratio of 1:4. What is the size of the smaller angle?

Possible Answers:

$144^{\circ}$

$18^{\circ}$

$72^{\circ}$

$36^{\circ}$

$45^{\circ}$

Correct answer:

$36^{\circ}$

Explanation:

Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:

$x+4x=180$

$5x=180$

$x=36^{\circ}$

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Example Question #1 : Plane Geometry

Varsity_question

AB and CD are two parrellel lines intersected by line EF. If the measure of angle 1 is 132^o , what is the measure of angle 2?

Possible Answers:

$24^{\circ}$

$64^{\circ}$

$48^{\circ}$

$180^{\circ}$

$132^{\circ}$

Correct answer:

$132^{\circ}$

Explanation:

The angles are equal. When two parallel lines are intersected by a transversal, the corresponding angles have the same measure.

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Example Question #2 : Geometry

Angles

Figure not drawn to scale.

In the figure above, APB forms a straight line. If the measure of angle APC is eighty-one degrees larger than the measure of angle DPB, and the measures of angles CPD and DPB are equal, then what is the measure, in degrees, of angle CPB?

Possible Answers:

114

Correct answer:

Explanation:

Let x equal the measure of angle DPB. Because the measure of angle APC is eighty-one degrees larger than the measure of DPB, we can represent this angle's measure as x + 81. Also, because the measure of angle CPD is equal to the measure of angle DPB, we can represent the measure of CPD as x.

Since APB is a straight line, the sum of the measures of angles DPB, APC, and CPD must all equal 180; therefore, we can write the following equation to find x:

x + (x + 81) + x = 180

Simplify by collecting the x terms.

3x + 81 = 180

Subtract 81 from both sides.

3x = 99

Divide by 3.

x = 33.

This means that the measures of angles DPB and CPD are both equal to 33 degrees. The original question asks us to find the measure of angle CPB, which is equal to the sum of the measures of angles DPB and CPD.

measure of CPB = 33 + 33 = 66.

The answer is 66.

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Example Question #4 : How To Find An Angle Of A Line

One-half of the measure of the supplement of angle ABC is equal to the twice the measure of angle ABC. What is the measure, in degrees, of the complement of angle ABC?

Possible Answers:

Correct answer:

Explanation:

Let x equal the measure of angle ABC, let y equal the measure of the supplement of angle ABC, and let z equal the measure of the complement of angle ABC.

Because x and y are supplements, the sum of their measures must equal 180. In other words, x + y = 180.

We are told that one-half of the measure of the supplement is equal to twice the measure of ABC. We could write this equation as follows:

(1/2)y = 2x.

Because x + y = 180, we can solve for y in terms of x by subtracting x from both sides. In other words, y = 180 – x. Next, we can substitute this value into the equation (1/2)y = 2x and then solve for x.

(1/2)(180-x) = 2x.

Multiply both sides by 2 to get rid of the fraction.

(180 – x) = 4x.

Add x to both sides.

180 = 5x.

Divide both sides by 5.

x = 36.

The measure of angle ABC is 36 degrees. However, the original question asks us to find the measure of the complement of ABC, which we denoted previously as z. Because the sum of the measure of an angle and the measure of its complement equals 90, we can write the following equation:

x + z = 90.

Now, we can substitute 36 as the value of x and then solve for z.

36 + z = 90.

Subtract 36 from both sides.

z = 54.

The answer is 54.

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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 #1 : Sin, Cos, Tan

Example Question #621 : New Sat

Example Question #1 : Trigonometric Operations

Example Question #11 : Sin, Cos, Tan

Example Question #11 : Sin, Cos, Tan

Example Question #11 : Sin, Cos, Tan

Example Question #1 : Plane Geometry

Example Question #1 : Plane Geometry

Example Question #2 : Geometry

Example Question #4 : How To Find An Angle Of A Line

All New SAT Math - Calculator Resources

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