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12. TRIGONOMETRIC IDENTITIES

12. TRIGONOMETRIC IDENTITIES. TRIGONOMETRIC IDENTITIES. An identity is an equation that is true for all defined values of a variable. We are going to use the identities to "prove" or establish other identities. . RECIPROCAL IDENTITIES. QUOTIENT IDENTITIES. PYTHAGOREAN IDENTITIES.

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12. TRIGONOMETRIC IDENTITIES

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  1. 12. TRIGONOMETRIC IDENTITIES

  2. TRIGONOMETRIC IDENTITIES An identity is an equation that is true for all defined values of a variable. We are going to use the identities to "prove" or establish other identities.

  3. RECIPROCAL IDENTITIES QUOTIENT IDENTITIES PYTHAGOREAN IDENTITIES

  4. Examples! The first type of examples are rewriting expressions (no = sign) Rewrite

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  11. Another type of example is verifying an identity You will use identities you already to know to prove an equation that you are given Always start with the more complicated side and work to make it equal to the other side Verify

  12. Verify the following identity: Let's sub in here using reciprocal identity In establishing an identity you should NOT move things from one side of the equal sign to the other. Instead substitute using identities you know and simplifying on one side until both sides match.

  13. Establish the following identity: Let's sub in here using reciprocal identity and quotient identity combine fractions Another trick is if you have two terms with one term a 1 and the other a sine or cosine, multiply top and bottom of the fraction by the conjugate and then you'll be able to use the Pythagorean Identity

  14. Hints for Establishing Identities • Work on the more complex side first • If there are 2 fractions, get a common denominator • If there is 1 fraction with 2 pieces on top and 1 on bottom, split into 2 • If you have squared functions look for Pythagorean Identities • If you can distribute, you should • If you can factor, you should • If you have a fraction with 1 + trig function try multiplying top & bottom by conjugate and use Pythagorean Identity • Write everything in terms of sines and cosines using reciprocal and quotient identities • Have fun with these---it's like a puzzle, can you use identities and algebra to get them to match!

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