Basic and Pythagorean Iden.ies. You can see the PythagoreanThereom 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 doubleangles and half angles. First we are going to concentrate on the double angles and examples. DoubleAngles 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 satised 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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