6.3– 6.6 Trigonometric (Circular) Functions The graph of y = c + a sin 3b1x - d24 or y = c + a cos 3b1x - d24, where b 70, has amplitude a , period 2p b , a vertical translation up c units if c 70 or down c units if c 60, and a phase shift to the right d units if d 70 or to the left d units if d 60. The graph of y = a tan bx or y = a cot bx has period p b , where b 70. x y 1 0 y = sin x –1 2p p 3p 2 p 2 x y 1 0 –1 y = cos x 2p p 3p 2 p 2 x y 0 y = tan x p 2 p 2 – x y 0 –1 1 y = csc x p 2 –p p p 2 – x y 0 –1 1 y = sec x p 2 –p p p 2 – y = cot x p 2 x y 0 p –1 1 p 2 p 2 – y = sin–1 x or y = arcsin x x y 0 p 2 p y = cos–1 x or y = arccos x x y 0 –1 1 p 2 p 2 – y = tan–1 x or y = arctan x x y 0 –2 –1 1 2 p 2 –p 2 y x –2 –1 0 1 2 y = csc–1 x or y = arccsc x –2 2 –1 0 1 y p x y = sec–1 x or y = arcsec x –2 2 –1 0 1 y p x y = cot–1 x or y = arccot x 7.5 Inverse Trigonometric (Circular) Functions
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