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Basic and Pythagorean Iden.ies. You can see the Pythagorean-Thereom relationship clearly if you consider the unit circle, where the angle is t, the "opposite" side is sin t = y, the "adjacent" side is cos t = x, and the hypotenuse is 1..The tangent tan of an angle is the ratio of the sine to the cosine: Finally, the reciprocal functions secant sec , cosecant csc , and cotangent cot are the reciprocals of the cosine, sine, and tangent: These definitions are sometimes referred to as ratio iden.ies..Sin theta = a / c. csc theta = 1 / sin theta = c / a. cos theta = b / c. sec theta = 1 / cos theta = c / b. tan theta = sin theta / cos theta = a / b. cot theta = 1/ tan theta = b / a. sin -x = -sin x csc -x = -csc x cos -x = cos x sec -x = sec x tan -x = -tan x cot -x = -cot x . sin2 x + cos2 x = 1. tan2 x + 1 = sec2 x . cot2 x + 1 .By using the sum and difference iden.ies for both sine and cosine, we are able to compile different types of double-angles and half angles. First we are going to concentrate on the double angles and examples. Double-Angles Iden.ies. Sum iden.y for sine: sin x + y = sin x cos y + cos x sin y sin x + x = sin x cos .

Tr.nometric iden.ies An iden.y is an equation that is satis-ed by all the values of the variable s in the equation. For example, the equation.Tr.nometric functions, iden.ies, formulas and the sine and cosine laws are presented..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 = 1 for all . 3. Tr.nometric Iden.ies and Equations, Solution Key Multiply by the reciprocal cosx 1 cosx cosx =cosx 1 2cosx cosx =cosx cosx 1 cosx=.

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    Tr.nometric iden.ies An iden.y is an equation that is satis-ed by all the values of the variable s in the equation. For example, the equation.

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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 = 1 for all .

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    3. Tr.nometric Iden.ies and Equations, Solution Key Multiply by the reciprocal cosx 1 cosx cosx =cosx 1 2cosx cosx =cosx cosx 1 cosx=.

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