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Published byMelina Evans Modified over 9 years ago
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7.6 – The Inverse Trigonometric Ratios Essential Question: How do you make a function without an inverse have an inverse?
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From chapter 4, we learned that for a function to be one-to-one and have an inverse it must pass the horizontal line test.
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If you look at the tangent graph, the graph of tan x is not one-to-one, so therefore has no inverse. However, if we restrict our domain, like in the second picture, it is one- to-one and thus has an inverse.
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Tangent Graph The inverse is the third picture and is denoted: f -1 (x) = Tan -1 x
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Example Find Tan -1 3 with a calc in a) degrees and b) radians.
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The inverse of the sine and cosine graphs: Pictures:
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Example: Find with calc: a. Sin -1 b. Cos -1 (-.2)
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Example: Find without using a calc: a. Tan -1 (–1) b. Tan -1 (1) c. Sin -1 d. Cos -1
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Examples: - Find sec (Tan -1 ) with a calc. - Find csc (Cos -1 ( )) using a graph (without a calc.).
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Example: - Find the approximate value and exact value of csc (Cos -1 ( -.4)).
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