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Lecture Notes Tr.nometric Iden.ies Sample Problems - Solutions 1. tanxsinx+cosx = secx Solution: We will only use the fact that sin2 x+cos2 x .Tr.nometric functions, iden.ies, formulas and the sine and cosine laws are presented..X=npi or x=2npi+-pi/3, where n is an integer sinx-2sinxcosx=0 hArrsinx 1-2cosx =0 Hence either sinx=0 i.e. x=npi, where n is an integer or 1-2cosx=0 i.e. cosx=1/2 and x=2npi+-pi/3, where n is an integer.Find sin 2x, knowing sin x = -3/5 Ans: 0.96 There are 2 ways: 1. First way. Calculator gives --> sin x = -3/5 = - 0.60 --> x = -36.87 deg and x = 180 + 36.87 = 216.87 Quadrant III Then, 2x = 2 216.87 = 433.74 = 73.74 + 360 deg --> --> sin 2x = sin 73.74 = 0.96 Second way sin x = -0.6 --> sin^2 x = 0.36 --> cos^2 x = 1 - 0.36 = 0.64 .

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    Lecture Notes Tr.nometric Iden.ies Sample Problems - Solutions 1. tanxsinx+cosx = secx Solution: We will only use the fact that sin2 x+cos2 x .

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    Tr.nometric functions, iden.ies, formulas and the sine and cosine laws are presented..

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    X=npi or x=2npi+-pi/3, where n is an integer sinx-2sinxcosx=0 hArrsinx 1-2cosx =0 Hence either sinx=0 i.e. x=npi, where n is an integer or 1-2cosx=0 i.e. cosx=1/2 and x=2npi+-pi/3, where n is an integer.

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    Find sin 2x, knowing sin x = -3/5 Ans: 0.96 There are 2 ways: 1. First way. Calculator gives --> sin x = -3/5 = - 0.60 --> x = -36.87 deg and x = 180 + 36.87 = 216.87 Quadrant III Then, 2x = 2 216.87 = 433.74 = 73.74 + 360 deg --> --> sin 2x = sin 73.74 = 0.96 Second way sin x = -0.6 --> sin^2 x = 0.36 --> cos^2 x = 1 - 0.36 = 0.64 .

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