3 6 Proving Trigonometric Identities Mrs Lisa Allen

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(3 -6) Proving Trigonometric Identities Mrs. Lisa Allen Honors Pre-calculus Saucon Valley High School

(3 -6) Proving Trigonometric Identities Mrs. Lisa Allen Honors Pre-calculus Saucon Valley High School

Strategies to use when proving identities 1) 2) 3) 4) Know the fundamental identities

Strategies to use when proving identities 1) 2) 3) 4) Know the fundamental identities Write expressions in terms of sines and cosines Refer to other side of identity intermittently If one side of the identity has only one trigonometric function, rewrite the other side in terms of that one trigonometric function 5) Use the Pythagorean Identities for expressions equal to 1. 6) Perform algebraic operations (on next page)

Perform Algebraic Operations 1) 2) 3) 4) 5) Factor Simplify complex rational expressions Find

Perform Algebraic Operations 1) 2) 3) 4) 5) Factor Simplify complex rational expressions Find the LCD and combine fractions Combine Like Terms Multiply the numerator and denominator by the same expression to obtain an equivalent fraction 6) Replace a binomial with a monomial

Proofs not Solving Equations 1. Do not use the addition or multiplication properties for

Proofs not Solving Equations 1. Do not use the addition or multiplication properties for equalities. 2. Work with each side of the identity independently until one side is identical to the other side.

Simplify Complex Fractions Multiply by the LCD/LCD

Simplify Complex Fractions Multiply by the LCD/LCD

Simplify Complex Fractions Multiply by the LCD/LCD

Simplify Complex Fractions Multiply by the LCD/LCD

Recognizing factoring of Perfect Square Trinomials

Recognizing factoring of Perfect Square Trinomials

Factor the following Trinomials 9 9 9 3 x 5

Factor the following Trinomials 9 9 9 3 x 5

Example 1 Prove the identity.

Example 1 Prove the identity.

Example 2 Prove the identity.

Example 2 Prove the identity.

Example 3 Prove the Identity ASIDE

Example 3 Prove the Identity ASIDE

Example 4 Prove the identity

Example 4 Prove the identity

Example 5 Prove the identity

Example 5 Prove the identity

Example 6 Prove the identity LCD= ASIDE

Example 6 Prove the identity LCD= ASIDE

Homework P. 143 Practice Exercises #s 3, 6, 9, 12, 15, 17, 21, 25,

Homework P. 143 Practice Exercises #s 3, 6, 9, 12, 15, 17, 21, 25, 28