# High School Math : Trigonometric Identities

## Example Questions

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### Example Question #113 : Trigonometry

What is the  of ?

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic:

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

### Example Question #1 : Trigonometric Identities

Simplify .

Explanation:

Simplifying trionometric expressions or identities often involves a little trial and error, so it's hard to come up with a strategy that works every time. A lot of times you have to try multiple strategies and see which one helps.

Often, if you have any form of    or  in an expression, it helps to rewrite it in terms of sine and cosine. In this problem, we can use the identities  and .

.

This doesn't seem to help a whole lot. However, we should recognize that  because of the Pythagorean identity .

We can cancel the  terms in the numerator and denominator.

.

### Example Question #15 : Graphs And Inverses Of Trigonometric Functions

What is the  of ?

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: .

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

### Example Question #16 : Graphs And Inverses Of Trigonometric Functions

What is the  of ?

Explanation:

When working with basic trigonometric identities, it's easiest to remember the mnemonic: .

When one names the right triangle, the opposite side is opposite to the angle, the adjacent side is next to the angle, and the hypotenuse spans the two legs of the right angle.

Simplify

Explanation:

.  Thus:

Simplify

Explanation:

and

.

### Example Question #117 : Trigonometry

Simplify .

Explanation:

Remember that . We can rearrange this to simplify our given equation:

### Example Question #121 : Trigonometry

Simplify:

This is the most simplified version.

Explanation:

Whenever you see a trigonometric function squared, start looking for a Pythagorean identity.

The two identities used in this problem are  and .

Substitute and solve.

### Example Question #1 : Using Identities Of Squared Functions

Factor and simplify .

This is already it's most reduced form.

Explanation:

To reduce , factor the numerator:

Notice that we can cancel out a .

This leaves us with .

Simplify .