# Precalculus : Trigonometric Functions

## Example Questions

### Example Question #5 : Prove Trigonometric Identities

Simplify

Explanation:

This expression is a trigonometric identity:

### Example Question #6 : Prove Trigonometric Identities

Simplify

Explanation:

Factor out 2 from the expression:

Then use the trigonometric identities  and  to rewrite the fractions:

Finally, use the trigonometric identity  to simplify:

### Example Question #7 : Prove Trigonometric Identities

Simplify

Explanation:

Factor out the common   from the expression:

Next, use the trigonometric identify  to simplify:

Then use the identify  to simplify further:

### Example Question #8 : Prove Trigonometric Identities

Simplify

Explanation:

To simplify the expression, separate the fraction into two parts:

The  terms in the first fraction cancel leaving you with:

Then you can deal with the remaining fraction using the rule that . This leaves:

You can separate this into:

And each half of this expression is now a trigonometric identity:  and . This gives you:

### 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 #1 : Find The Decimal Value Of A Trigonometric Function

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