New SAT Math - Calculator : New SAT Math - Calculator

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

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Example Questions

Example Question #2 : Sin, Cos, Tan

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

Possible Answers:

Correct answer:

Explanation:

Because  is an odd function, we can rewrite the second term in the expression.

.

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

.

Because they are reciprocals, .

Example Question #1 : Sine, Cosine, & Tangent

Round to the nearest hundredth. 

Use your calculator to find:

 

Possible Answers:

None of the above

Correct answer:

Explanation:

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

Plug in  which equals to .

Example Question #1 : Sin, Cos, Tan

Round to the nearest hundredth. 

Use your calculator to find:

Possible Answers:

None of the above

Correct answer:

Explanation:

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

plug in 

 

which is equal to .

Example Question #11 : Sin, Cos, Tan

What is the value of cos30o . sin30o . tan60o

Possible Answers:

Correct answer:

Explanation:

Solution

Example Question #12 : Trigonometric Operations

 What is the closest value to this expression?

Possible Answers:

Correct answer:

Explanation:

First you have to know the equation for   and apply it to our equation. Second the formula of  will allow you to get rid of the square sin and cos. Third the equation  will allow you to get rid of the . Therefore, we will have a , and that will be equal to . Sum  and  and you will get 

Example Question #12 : Sin, Cos, Tan

if   What is ?

Possible Answers:

Correct answer:

Explanation:

Remember two things. First if , find the by using the Pythagoras Theorem. If one side is  and the hypotenuse is , then the other side is  will be . Finally remember the formula for . And just place the things we found to the equation.

Example Question #1 : How To Find An Angle Of A Line

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

Possible Answers:

45^{\circ}

72^{\circ}

144^{\circ}

36^{\circ}

18^{\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}

Example Question #1 : How To Find An Angle Of A Line

Varsity_question

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

Possible Answers:

Correct answer:

Explanation:

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

Example Question #1 : 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:

66

50

33

114

40

Correct answer:

66

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.

Example Question #1 : Plane Geometry

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:

54

90

72

36

18

Correct answer:

54

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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