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Lecture 6

# MTH 162 Lecture 6: 5.6 Inverse Trigonometric Functions Notes Premium

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School
University of Miami
Department
Mathematics
Course
MTH 162
Professor
Pachero
Semester
Fall

Description
MTH 162 Calculus II 5.6 Inverse Trigonometric Functions Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section. Functions and Their Inverses What are the two main functions? f ▯1(f (x)) = x f f ▯1 (x) = x What are the properties of those two functions? ▯ ▯ ▯ f▯1 (f (x)) = x and f f1(x) = x ▯1 – f ▯ (f (x▯) = x would occur every x that’s in f’s domain. – f f ▯1 (x) = x for every x that’s in f’s domain ▯ Domain and Range ▯1 – f’s domain = f ’s range – f’s range = f▯1’s domain ▯1 ▯ Both f’s and f ’s graph are symmetric, but with respect to the line y = x. ▯ If and Then – If you have a function has its own inverse function, then the implicit equation of the inverse function would be x = f(y). – If you are solving the given equation for y, then you would have to obtain the explicit equation that would look like y =(x). Inverse Sine Function ▯1 y = sin (x) x = sin(y) ▯1 ▯ x ▯ 1 ▯ ▯ ▯ ▯ y ▯ 2 2 1 Properties f ▯1(f (x)) = sin (sin(x)) = x ▯ ▯ ▯ x ▯ ▯ 2 2 ▯ ▯1 ▯ ▯ ▯1 ▯ f f (x) = sin sin (x) = x ▯1 ▯ x ▯ 1 Inverse Cosine Function y = cos▯1(x) x = cos(y) ▯1 ▯ x ▯ 1 0 ▯ y ▯ ▯ Properties ▯1 ▯1 f (f (x)) = cos (sin(x)) = x 0 ▯ x ▯ ▯ ▯ ▯ ▯ ▯ f f ▯1(x) = sin sin ▯1(x) = x ▯1 ▯ x ▯ 1 Inverse Tangent Function y = tan▯1(x) x = tan(y) ▯1 ▯ x ▯ 1 ▯ ▯ ▯ y ▯ ▯
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