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Calculus Section 5.6 Inverse Trig Functions -Develop properties of the six inverse trigonometric functions Homework: page 377 #’s 5 – 27 odd, 31, 32, 33 (Hint: #33 take the sin of both sides first) Fact: None of the six basic trigonometric functions (sin, cos, …) has an inverse functions. This is because all trig functions are ___________________ and thus not _________________________. However, you can ___________________ the domain for the trig functions to allow them to have an inverse. For example, the sine function is one-to-one if its domain is restricted to __________________. Then, then inverse function of sine is defined as: The Six Trig and Inverse Trig Functions sinx cosx arcsinx arccosx arctanx cscx secx cotx arccscx arcsecx arccotx tanx The inverse function arcsin can also be written as: By definition, y = arcsin(-1/2) implies: Properties of Inverse Trig Functions If each trig function is restricted to its one-to-one domain, the following properties are true: If -1 ≤ x ≤ 1 and –π/2 ≤ y ≤ π/2, then If –π/2 < y < π/2, then If -1 ≤ x ≤ 1 and 0 ≤ y < π/2 or π/2 < y ≤ π, then Similar properties hold for the other inverse functions on their restricted domains. Examples 1) arctan(2x – 3) = π/4 4) Find cos[arcsin(x)] 2) arcos(0) = 5) Given y = arcsec( 3) sin-1(x2) = π/2 5 ), find tan(y). 2