7 6 Exploration Trig Identities Honors Analysis Learning

Use the triangle below to prove the identity shown above. Hint: How can

Strategies for simplifying trigonometric expressions Write trig functions in term of sin/cos/tan Look for

Trig Identity Tips Make obvious replacements Convert reciprocal functions to sin/cos/tan where possible If

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7. 6 Exploration: Trig Identities Honors Analysis Learning Target: I can develop trigonometric identities

Identity #1:

Identity #2:

Use the triangle below to prove the identity shown above. Hint: How can the hypotenuse be labeled using a and b?

Deriving the Pythagorean Identities:

Trig Identities Summary:

Simplify:

Strategies for simplifying trigonometric expressions Write trig functions in term of sin/cos/tan Look for Pythagorean identities (may need to factor out GCF to find) Fractions: Find a common denominator & combine Fractions: Break up a sum/difference in the numerator as two fractions with the same denominator

Verify the trig identity

Verify the trig identity:

Trig Identity Tips Make obvious replacements Convert reciprocal functions to sin/cos/tan where possible If factored, multiply out If not factored, factor out GCF Try converting all values to sin/cos form If there is a sum or difference in the numerator, split it up into two fractions (CAREFUL!! You can’t split up denom!) Sum/difference of fractions – find common denominator and add

Multiple Angle Identities

Simplify

Evaluate:

Ch. 7 Test Review: Identities

Simplify:

Simplify: sin �� cot ��

Simplify: