SAT II Math I : Sine, Cosine, Tangent

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #1 : Sine, Cosine, Tangent

Solve for between .

 

Possible Answers:

Correct answer:

Explanation:

First we must solve for when sin is equal to 1/2. That is at

Now, plug it in:

Example Question #2 : Sine, Cosine, Tangent

Solve for between .

Possible Answers:

 
Correct answer:

Explanation:

First we must solve for when sin is equal to 1/2. That is at

Now, plug it in:

Example Question #3 : Sine, Cosine, Tangent

In a triangle, , what is the measure of angle A if the side opposite of angle A is 3 and the adjacent side to angle A is 4?

(Round answer to the nearest tenth of a degree.)

Possible Answers:

Correct answer:

Explanation:

To find the measure of angle of A we will use tangent to solve for A. We know that

In our case opposite = 3 and adjacent = 4, we substitute these values in and get:

Now we take the inverse tangent of each side to find the degree value of A.

Example Question #4 : Sine, Cosine, Tangent

If , what is  if  is between  and ?

Possible Answers:

Correct answer:

Explanation:

Recall that .

Therefore, we are looking for  or .

Now, this has a reference angle of , but it is in the third quadrant. This means that the value will be negative. The value of  is . However, given the quadrant of our angle, it will be .

Example Question #5 : Sine, Cosine, Tangent

Determine the exact value of .

Possible Answers:

Correct answer:

Explanation:

The exact value of  is the x-value when the angle is 45 degrees on the unit circle.  

The x-value of this angle is .

Example Question #6 : Sine, Cosine, Tangent


Sine

Which of the following is equal to cos(x)?

Possible Answers:

Correct answer:

Explanation:

Remember SOH-CAH-TOA! That means:

                      

                                       

                      

sin(y) is equal to cos(x)

Example Question #1 : Sin, Cos, Tan

Find the value of .

Possible Answers:

Correct answer:

Explanation:

To find the value of , solve each term separately.

Sum the two terms.

Example Question #3 : Trigonometric Operations

Calculate .

Possible Answers:

Correct answer:

Explanation:

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

for all .

Since , we can rewrite the original expression  as follows:

                 

                 

                 

                 

Hence, 

Example Question #4 : Trigonometric Operations

Calculate .

Possible Answers:

Correct answer:

Explanation:

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

Next, recall that  lies in the fourth quadrant of the unit circle, wherein the cosine is positive. Furthermore, the reference angle of  is 

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

,

which is .

Therefore,

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