Precalculus : Double-Angle Identities

Example Questions

Example Question #1 : Double Angle Identities

Find the exact value

.

Explanation:

By the double angle formula

Example Question #2 : Double Angle Identities

Find the exact value

.

Explanation:

By the double angle formula

Example Question #3 : Double Angle Identities

Find the exact value

.

Explanation:

By the double-angula formula for cosine

For this problem

Example Question #4 : Double Angle Identities

Find the exact value

.

Explanation:

By the double-angle formula for the sine function

we have

thus the double angle formula becomes,

Example Question #5 : Double Angle Identities

If , which of the following best represents ?

Explanation:

The expression  is a double angle identity that can also be rewritten as:

Replace the value of theta for .

Example Question #6 : Double Angle Identities

Which expression is equivalent to  ?

Explanation:

The relevant trigonometric identity is:

In this case, "u" is since .

The only one that actually follows this is