• identity

• trigonometric identity

• cofunction

• odd-even identities

BELLRINGER: Define each word in your notebook.

Use Reciprocal and Quotient Identities

A. If , find sec θ.

Divide.

Reciprocal Identity

Answer:

Use Reciprocal and Quotient Identities

B. If and , find sin x.

Reciprocal Identity

Quotient Identity

Substitute for cos x.

Use Reciprocal and Quotient Identities

Answer:

Divide.

Multiply each side by .

Simplify.

Use Pythagorean Identities

If cot θ = 2 and cos θ < 0, find sin θ and cos θ.

cot 2 θ + 1= csc

2 θ Pythagorean Identity(2)

2 + 1= csc 2 θ

cot θ = 25 = csc

2 θ Simplify.

Use the Pythagorean Identity that involves cot θ.

= csc θ Take the square root of each side. Reciprocal Identity

Solve for sin θ.

Use Pythagorean Identities

Since is positive and cos θ < 0, sin θ

must be negative. So . You can

then use this quotient identity again to find cos θ.

Quotient Identity

cot θ = 2 and

Multiply each side by .

Use Pythagorean Identities

So,

Check sin 2 θ + cos 2 θ= 1Pythagorean Identity

Answer:

Simplify.

Use Cofunction and Odd-Even Identities

Simplify.cos x = –0.75Cofunction Identity

If cos x = –0.75, find

Odd-Even Identity

Factor.

Use Cofunction and Odd-Even Identities

Answer: 0.75

So, = 0.75.

Simplify by Rewriting Using Only Sine and Cosine

Solve Algebraically

Simplify .

Simplify.

Multiply.

Pythagorean Identity

So, = cos x.

Simplify by Factoring

Simplify cos x tan x – sin x cos 2 x.

Solve Algebraicallycos x tan x – sin x cos

2 x Original expression

Factor.

Multiply.

Quotient Identity

So, cos x tan x – sin x cos 2 x = sin3 x.

Pythagorean Identity

Simplify.= sin3x

Simplify by Combining Fractions

Common denominator

Multiply.

Add the numerators.

Simplify.

Pythagorean Identity

Simplify .

Answer: – 2 sec2 x – 2 sec2 x

Simplify by Combining Fractions

Reciprocal Identity

Reciprocal Identity

–2csc2 x.

Divide out common factor.

Reciprocal and Quotient Identities

Rewrite to Eliminate Fractions

Rewrite as an expression that does not

involve a fraction.

Pythagorean Identity

Reciprocal Identity

Quotient Identity

Reciprocal Identity

Rewrite to Eliminate Fractions

Answer: tan 2 x

So, = tan2 x.