High School Math : Using Basic and Definitional Identities

Example Questions

Example Question #1 : Using Basic And Definitional Identities

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 #2 : Using Basic And Definitional 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 #3 : Using Basic And Definitional Identities

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 #4 : Using Basic And Definitional Identities

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.