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- 7.3 Sum and Difference Identities. Previous Identities Reciprocal Identities Quotient Identities Pythagorean Identities Negative-Number Identities Note

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7.3 Sum and Difference IdentitiesPrevious IdentitiesReciprocal Identities

Quotient Identities

Pythagorean Identities

Negative-Number Identities

Note It will be necessary to recognize alternative forms of the identities above, such as sin = 1 cos and cos = 1 sin .

Combined Sum and Difference Formulas

ExampleFind the exact value of the following.cos 15

cos

(or 60 45)ExampleFind the exact value of the following.sin 75tan sin 40 cos 160 cos 40 sin 160

Solution(a)

(b)

(c) sin 40cos 160 cos 40sin 160 =sin(40-160) = sin(120)

Find the exact value of each expression:

=0

=1

Undefined

EXAMPLE:Find the exact value of ( cos 80 cos 20 + sin 80 sin 20) . Solution The given expression is the right side of the formula for cos( - ) with = 80 and = 20. cos 80 cos 20 + sin 80 sin 20 = cos (80 - 20) = cos 60 = 1/2cos( -) = cos cos + sin sin ExampleExample

Write the following expression as the sine, cosine, or tangent of an angle. Then find the exact value of the expression.Solution:

Evaluating a Trigonometric EquationFind the exact value of :

An Application of a Sum FormulaWrite as an algebraic expression

Proving a Cofunction Identity

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