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

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Presentation transcript:

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:

sin cot

Simplify: