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Chapter 5: Trigonometric Functions

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.

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Chapter 5: Trigonometric Functions

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

  2. 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.

  3. 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 1. • 3. Make the function continuous (no breaks), if possible.

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

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

  6. 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.

  7. 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 1. • 3. Make the function continuous (no breaks), if possible.

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

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

  10. 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?

  11. 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.

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

  13. Examples 1 & 2 • Find the exact value of • Find the exact value of

  14. 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

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