# Precalculus : Evaluating Trig Functions

## Example Questions

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### Example Question #1 : Evaluating Trig Functions

Find the value of  to the nearest tenth if  and .

Explanation:

Rewrite  in terms of sine and cosine.

Substitute the known values and evaluate.

The answer to the nearest tenth is .

### Example Question #2 : Evaluating Trig Functions

Determine the value of  in decimal form.

Explanation:

Ensure the calculator is in radian mode since the expression shows the angle in terms of .  Also convert cotangent to tangent.

### Example Question #3 : Evaluating Trig Functions

Find the decimal value of

Explanation:

To determine the decimal value of the following trig function, , make sure that the calculator is in radian mode.

Compute the expression.

### Example Question #4 : Evaluating Trig Functions

Determine the correct value of

.

Explanation:

The question  asks for the y-coordinate on the unit circle when the degree angle is .

Be careful not to confuse finding the value of the angle when the y-value of the coordinate of the unit circle is .

Ensure that the calculator is in degree mode.

### Example Question #5 : Evaluating Trig Functions

Find the value of

.

Explanation:

Before beginning this problem on a calculator, though this is not necessary since these are special angles, ensure that the mode of the calculator is in degrees.

Input the values of the expression and solve.

### Example Question #1 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known

Solve for all x on the interval

,

,

,

,

,

Explanation:

Solve for all x on the interval

We can begin by recalling which two quadrants have a positive sine. Because sine corresponds to the y-value, we know that sine is positive in quadrants I and II.

Next, recall where we get .

always corresponds to our -increment angles. In this case, the angles we are looking for are  and , because those are the two -increment angles in the first two quadrants.

Now, you might be saying, "what about ? That is an increment of 45."

While that is true, , not

,

### Example Question #2 : Find The Degree Measure Of An Angle For Which The Value Of A Trigonometric Function Is Known

Solve for all x on the interval

Explanation:

Solve for all x on the interval

Remember Soh, Cah, Toa?

For this problem it helps to recall that

Since our tangent is equal to 1 in this problem, we know that our opposite and adjacent sides must be the same (otherwise we wouldn't get "1" when we divided them)

Can you think of any angles in the first quadrant which yield equal x and y values?

If you guessed  you guessed right! Remember that your  angle in the unit circle will give you a  triangle, which will have equal height and base.

### Example Question #8 : Evaluating Trig Functions

The above triangle is a right triangle. Find the value of  (in degrees).

Explanation:

One can setup the relationship

After taking the arccosine,

the arccosine cancels out the cosine leaving just the value of .

### Example Question #9 : Evaluating Trig Functions

What is the value of  (in degrees)?

Explanation:

One can setup the relationship

.

After taking the arctangent,

the arctangent cancels out the tangent and we are left with the value of .

Solve for :

or

or

or

or

or