Chapter 5: Trigonometric Functions Lessons 3, 5, 6: Inverse Cosine, Inverse Sine, and Inverse Tangent functions Mrs. Parziale.

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Chapter 5: Trigonometric Functions Lessons 3, 5, 6: Inverse Cosine, Inverse Sine, and Inverse Tangent functions Mrs. Parziale

Graph y = cos (x). Notice that since it fails the HLT, its inverse is not a function. Restrict it so that the section contains the entire range (-1 to 1) and passes the HLT.

When restricting the domain, the following qualifications must be met: 1. Must include the values from 0 degrees to 90 degrees (to represent all acute angles that are possible in a right triangle.) 2. Must include the entire range of the cosine graph from -1 to Make the function continuous (no breaks), if possible.

Plot the Inverse Function Find the domain and range of each. Domain:Domain: Range:Range:

Example 1 & 2: Evaluate (exact answer) Evaluate, give an answer in degrees (approximate)

Graph y = sin (x). Notice it fails the HLT, so the inverse is not a function. Restrict it so that the section contains the entire range (-1 to 1), and passes HLT.

When restricting the domain, the following qualifications must be met: 1. Must include the values from 0 degrees to 90 degrees (to represent all acute angles that are possible in a right triangle.) 2. Must include the entire range of the sine graph from -1 to Make the function continuous (no breaks), if possible.

Plot the Inverse Function Find the domain and range of each. Domain:Domain: Range:Range:

Examples 1, 2, & 3 Find the exact value of Find the exact value of Arcsin 1

Graph y = tan (x). Does this function pass the HLT? How do we restrict the tangent function so that the inverse is also a function and the entire range is contained (as the domain) in the new function?

When restricting the domain, the following qualifications must be met: 1. Must include the values from 0 degrees to 90 degrees (to represent all acute angles that are possible in a right triangle.) 2. Must include the entire range of the tangent graph. (all reals) 3. Make the function continuous (no breaks), if possible.

Find the domain and range of each. Domain:Domain: Range:Range: Plot the Inverse Function

Examples 1 & 2 Find the exact value of

Closure Name three conditions that must be true when restricting the domain of the trig functions to graph the inverse functions? Looking at the unit circle, what quadrants is cosine restricted to? Sine? Tangent? Try these