You found trigonometric values using the unit circle. (Lesson 4-3)

You found trigonometric values using the unit circle. (Lesson 4-3) LEQ: How do we identify and use basic trigonometric identities to find trigonometric values & use basic trigonometric identities to simplify and rewrite trigonometric expressions?

identity trigonometric identity cofunction odd-even identities

Use Reciprocal and Quotient Identities A. If, find sec θ. Reciprocal Identity Divide. 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 Divide. Multiply each side by. Simplify. Answer:

If, find sin. A. B. C. D.

Use Pythagorean Identities If cot θ = 2 and cos θ < 0, find sin θ and cos θ. Use the Pythagorean Identity that involves cot θ. cot 2 θ + 1 = csc 2 θ (2) 2 + 1 = csc 2 θ cot θ = 2 5 = csc 2 θ Simplify. Pythagorean Identity = 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, Answer:

Use Pythagorean Identities So, Answer: Check sin 2 θ + cos 2 θ = 1 Pythagorean Identity Simplify.

Find the value of csc and cot if cos < 0. and A. B. C. D.

If cos x = 0.75, find Use Cofunction and Odd-Even Identities Factor. Odd-Even Identity Cofunction Identity cos x = 0.75 Simplify.

So, = 0.75. Use Cofunction and Odd-Even Identities Answer:

So, = 0.75. Use Cofunction and Odd-Even Identities Answer: 0.75

If cos x = 0.73, find. A. 0.73 B. 0.68 C. 0.68 D. 0.73

Solve Algebraically Simplify by Rewriting Using Only Sine and Cosine Simplify. Pythagorean Identity Multiply. Simplify. So, = cos x.

Simplify by Rewriting Using Only Sine and Cosine Support Graphically The graphs of appear to be identical. and y = cos x Answer:

Simplify by Rewriting Using Only Sine and Cosine Support Graphically The graphs of appear to be identical. and y = cos x Answer: cos x

Simplify csc x cos x cot x. A. cot x B. tan x C. cos x D. sin x

Simplify by Factoring Simplify cos x tan x sin x cos 2 x. Solve Algebraically cos x tan x sin x cos 2 x = sin 3 x Original expression Quotient Identity Multiply. Factor. So, cos x tan x sin x cos 2 x = sin 3 x. Pythagorean Identity Simplify.

Support Graphically Simplify by Factoring The graphs below appear to be identical. Answer:

Support Graphically Simplify by Factoring The graphs below appear to be identical. Answer: sin 3 x

Simplify cos 2 x sin x cos(90 x). A. sin 3 x B. sin 3 x C. cos 2 x 1 D. sin x cos x

Simplify by Combining Fractions Simplify. Common denominator Multiply. Add the numerators. Simplify. Pythagorean Identity

Simplify by Combining Fractions Reciprocal Identity Reciprocal and Quotient Identities Divide out common factor. 2csc 2 x. Reciprocal Identity Answer:

Simplify by Combining Fractions Reciprocal Identity Reciprocal and Quotient Identities Divide out common factor. 2csc 2 x. Reciprocal Identity Answer: 2 sec 2 x 2 sec 2 x

Simplify. A. cos x B. 2 + 2 cos x C. 2 sin x D. 2 csc x

Rewrite to Eliminate Fractions Rewrite as an expression that does not involve a fraction. Pythagorean Identity Reciprocal Identity Reciprocal Identity Quotient Identity

So, = tan 2 x. Rewrite to Eliminate Fractions Answer:

So, = tan 2 x. Rewrite to Eliminate Fractions Answer: tan 2 x

Rewrite as an expression that does not involve a fraction. A. 2 tan 2 x B. 1+ sin x C. 1 cos x D. 2 sin x