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8.2 Inverse Trigonometric Functions

Why are we learning this? We can solve trigonometric equations using inverse trigonometric functions How did we solve before?. 8.2 Inverse Trigonometric Functions. Function test for y=x, y=x 2 , y= sinx. Let us restrict the domain!. Learning Targets: Review Inverse functions

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8.2 Inverse Trigonometric Functions

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  1. Why are we learning this? We can solve trigonometric equations using inverse trigonometric functions How did we solve before? 8.2 Inverse Trigonometric Functions Function test for y=x, y=x2, y=sinx Let us restrict the domain! Learning Targets: Review Inverse functions Learn to define the domain and range of the inverse trigonometric functions Use inverse trigonometric function notation

  2. Inverse Sine Function Now will this restricted sine function have an inverse function? What do the input and output values of the sine and arcsine represent?

  3. Inverse Sine Function Example 1: Special Values – No Calculator Many answers but pick the one that is in the range of sin-1

  4. Properties of Inverse Sine What do these intervals represent? Example 2: Composition of Inverse Functions Explain not just by the rule but with logic Sketch a cosine function and think how we can restrict the domain in order to pass the horizontal line test

  5. Inverse Cosine Function Restricted cosine function: Same definition and properties apply to the inverse cosine…Just different domain and range. Domain: Range:

  6. Example 4: Equivalent Algebraic Expressions What will the value of cos-1 v represent? Fill in the missing side lengths of the triangle:

  7. Inverse Tangent Function Restricted tangent function: What is the domain? Range? Inverse tangent function: Domain: Range:

  8. Example 5: Evaluating Inverse Tangent Expressions Example 6: Exact Values 8.2 Hmwr:

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