# SAT II Math I : Sine, Cosine, Tangent

## Example Questions

### Example Question #1 : Trigonometry

Solve for between .

Explanation:

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

Now, plug it in:

### Example Question #1 : Trigonometry

Solve for between .

Explanation:

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

Now, plug it in:

### Example Question #1 : Trigonometry

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.)

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 #5 : Understanding Sine, Cosine, And Tangent

If , what is  if  is between  and ?

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 #1 : Sine, Cosine, Tangent

Determine the exact value of .

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 .

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

Explanation:

Remember SOH-CAH-TOA! That means:

### Example Question #4 : Sin, Cos, Tan

Find the value of .

Explanation:

To find the value of , solve each term separately.

Sum the two terms.

### Example Question #11 : Trigonometry

Calculate .

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 #1 : Sin, Cos, Tan

Calculate .

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,