Warm-up 8/22 Verify that the equation is an identity.

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Presentation transcript:

Warm-up 8/22 Verify that the equation is an identity. sin x tan x = sec x – cos x 1 = tan x cos x csc x Find a numerical value of one trig function 3. cos x csc x = 1

2.3 Sum and difference identities

Ex: Use the sum or difference identity to find the exact value of tan 735° Subtract 360 until you find the angle between 0 and 360 Express the angle using known angles (special triangles, unit circle) Use the identity Evaluate each trig value Get c.d. Mult by recip. rationalize Finished on next slide

Ex continued distribute Combine like terms, simplify

Ex: find exact value for You can change to degrees, if that is easier to work with Plug into formula for sinq, you will flip at the end. (sin45)(cos30)+(cos45)(sin30) This is sinq so flip to get cscq Can’t have radicals in denominator so mult numerator and denominator by

Ex. Find the EXACT value of sin(x + y) if , sin x = , and sin y = Means we are in QUAD I Write formula: sinx cosy + cosx siny Plug in what we know: Draw triangles to find what we don’t know 7 13 x2+72=132 9 17 x2+92=172 y x

Ex. Verify the identity. Use the reciprocal identity. Use the sum of sines identity. Evaluate trig functions. Simplify. Done!

2.3 Assignment p. 442 #15 – 41 odds SHOW WORK