Section 4 6 Inverse trigonometric functions Inverse sine function arcsin x sin 1 x y sin y x DOMAIN 1 x 1 RANGE 2 y 2 CANCELLATION EQUATIONS sin 1 sin x x for x 2 2 sin sin 1 x x for 1 x 1 Example 1 Find 1 sin 1 0 5 2 sin 1 sin 1 3 sin 2 sin 1 53 4 arcsin sin 5 4 1 Example 2 Simplify tan sin 1 x sin 1 x Inverse cosine function 1 1 x2 arccos x cos 1 x y cos y x DOMAIN 1 x 1 RANGE 0 y CANCELLATION EQUATIONS cos 1 cos x x for 0 x cos cos 1 x x for 1 x 1 cos 1 x Inverse tangent function 1 1 x2 arctan x tan 1 x y tan y x DOMAIN x RANGE 2 y 2 2 CANCELLATION EQUATIONS tan 1 tan x x for x 2 2 tan tan 1 x x for x lim tan 1 x x 2 lim tan 1 x x 2 1 tan 1 x 1 x2 Inverse cotangent function arccotx cot 1 x y cot y x DOMAIN x RANGE 0 y CANCELLATION EQUATIONS cot 1 cot x x for 0 x cot cot 1 x x for x lim cot 1 x 0 x lim cot 1 x x cot 1 x 1 1 x2 Other inverse trigonometric functions csc 1 x y csc y x DOMAIN x 1 3 RANGE y 0 2 3 2 1 csc 1 x x x2 1 sec 1 x y sec y x DOMAIN x 1 RANGE y 0 2 3 2 1 sec 1 x x x2 1 Example 3 Differentiate each function 1 f x sin 1 2x 1 2 g x x cos 1 x 1 x2 3 h x sin 1 tan 1 x 4 u t 2csc 1 t 4
View Full Document
Unlocking...