Section 6.1 - Section 6.1 The Inverse Sine, Cosine, and...

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Unformatted text preview: Section 6.1 The Inverse Sine, Cosine, and Tangent Functions Inverse of a function Recall that any 1-1 function has an inverse. We say that f -1 is an inverse of f if f(f -1(x))=x and f -1(f(x))=x Another way to think of it is that f(x)=y takes an x value to a y value And f -1(y)=x takes the y value to the x value Inverse sin Since the sin function is periodic we can restrict its domain and use that to represent the entire function. We restrict the domain of sin to [-/2, /2]. Inverse sin y=sin-1x implies x=sin y Where -1x 1 and -/2 y /2 To find the exact value of the inverse of sin you simply consider what angle you would need to get that value from sin. Inverse cos For cos we restrict the domain to [0, ] Inverse tan For tan we restrict our domain to [-/2, /2]. Section 6.2 The remaining inverse trigonometric functions The remaining inverse functions y=sec-1x implies x=sec y Where |x| 1 and 0 y , y /2 y=csc-1x implies x=csc y Where |x| 1 and -/2 y /2 y 0 y=cot-1x implies x=cot y Where - x and 0y ...
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