Trigonometry (Continued) Summary

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• Trigonometric equations

-  sin q = 0 Þ q = np, n Î Z

-  tan q = 0 Þ q = np, n Î Z

• If a is some constant angle, then

-    sin q = sin a Þ q = np + (-1)ⁿ a, n Î Z

-    cos q = cos a Þ q = 2np ± a, n Î Z

-    tan q = tan a Þ q = np + a, n Î Z

•  If a is some constant angle, then

-    sin² q = sin² a Þ q = n p ± a, n Î Z-    cos² q = cos² a Þ q = n p ± a  , n Î Z  

-    tan² q = tan² a Þ q = n p ± a , n Î Z

Relation between sides and angles of a triangle

•  If ABC is a triangle with sides a = BC, b = CA, c = AB, then

•  

-    a = b cos C + c cos B

-    b = c cos A + a cos C                       (Projection formula)

-    c = a cos B + b cos A

•  

Definitions of inverse trigonometric functions

Some properties of inverse trigonometric functions

In the principle value branches, the following formulae holds:

•  

-    sin^-1 (sin x) = x

-    cos^-1 (cos x) = x

-    tan^-1 (tan x) = x

-    cos^-1 (cot x) = x

-    sec^-1 (secx) = x

-    cosec^-1 (cosecx) = x

-     sin^-1 (-x) = -sin^-1 x

-     cos^-1 (-x) = p - cos^-1 x

-     tan^-1 (-x) = -tan^-1 x

-     cot^-1 (-x) = p -cot^-1 x

-     sec^-1(-x) = p - sec^-1 x

-     cosec^-1 (-x) = -cosec^-1 x