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TRIG IDENTITIES Section 5.8

3 Identities to Memorize: sin2Ө + cos2Ө = 1 1 + tan2Ө = sec2Ө 1 + cos2Ө = csc2Ө

tan2Ө means (tanӨ)2 Example If tanӨ=20˚, then tan2Ө = (20˚)2 ***NOTE tan2Ө means (tanӨ)2 Example If tanӨ=20˚, then tan2Ө = (20˚)2

Example 1 If tanӨ = 4/9, find secӨ Which identity would you use? The one that mentions tan and sec!!

Example 1 If tanӨ = 4/9, find secӨ 1 + tan2Ө = sec2Ө 1 + (4/9)2 = sec2Ө 81 + 16 = sec2Ө 81 81 97 = sec2Ө 81 secӨ = √97 9

Example 2 If sinӨ = 6/10, find cosӨ Which identity would you use? The one that mentions sin and cos!!

Example 2 If sinӨ = 6/10, find cosӨ sin2Ө + tan2Ө = 1 (6/10)2 + cos2Ө = 1 cos2Ө = 100 - 36 100 100 cos2Ө = 64 100 cosӨ = 8 or -8 10 10

Example 3 Reduce the following identity to a single term: csc2Ө - cot2Ө - sin2Ө = (1 + cot2Ө) - cot2Ө -sin2Ө = 1 - sin2Ө = cos2Ө

Example 4 Reduce the following to a single term: cosx ∙ cscx = cosx ∙ 1 sinx = cosx = cotx

HOMEWORK Workbook p.244-245 #3, 4, 8