Question

Precalculus Complete the function function and the domain andre dagas Module 7: Investigation 10 machin e diagrams by identifying the each function. Inverse Trigonometric Functions ingput and output quantities for cach for each sin Domain: Range: cos Domain: Range: Domain Range b. What is the input quantity for the inverse relation of the sine function? c. What is the output quantity for the inverse relation of the sine function? d. Is the inverse relation of the sine function a function itself (i.e., does cach vertical distance above the horizontal diameter produce a unique angle measure)? Explain. When considering the inverse sine function (or the arcsine function) we first restrict the domain ofthe sine function to- The Inverse Sine Function The inverse sine function takes as its input the vertical distance of the terminal point above the horizontal diameter (a sine value) and outputs a single angle measure that produces that sine value. 2 We write this function as 0- arcsin(y) or in(y). The Inverse Cosine Function the arccosine function) we first restrict the nction) we first restrict the hen considering the inverse tangent function (or the arctam funcr When co domain of the sine function to-f θα inverse tangent function takes as its input the slope of the t and outputs a single angle measure that produces that tangenterminal s that tangent value. gent valuc) We write this function as θ-arctan(n) or e-tan" (m) e. Complete the function machine diagrams by identifying the input and o function and the domain and range of each function. Domain Range Domain Range Domain 2. a. Demonstrate on the following circles how we can estimate the value of sin'(025) 0.5 05 b. Use your calculator to evaluate sin (0.25). Explain why the answer your calculator gives makes sense c. Your calculator only returns one possible value for sin (0.25). What other angle measures have a sine value of 0.25? Give at least two. Pathways Precalculus Page 28 C 2018 Carlson, Ochrtman, and Moore

Answer 1

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