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6.4 Inverses of the Trigonometric Functions Day 1

6.4 Inverses of the Trigonometric Functions Day 1. Do Now Solve for x Sin x = -1/2 Tan x = 1. Quiz Review. Retakes by?. Inverse Trig Functions. Recall: how to find inverse functions (switch x and y) Problem: If we switch x and y, the inverse fails the vertical line test

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6.4 Inverses of the Trigonometric Functions Day 1

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  1. 6.4 Inverses of the Trigonometric FunctionsDay 1 Do Now Solve for x Sin x = -1/2 Tan x = 1

  2. Quiz Review • Retakes by?

  3. Inverse Trig Functions • Recall: how to find inverse functions (switch x and y) • Problem: If we switch x and y, the inverse fails the vertical line test • (Draw picture here)

  4. Inverse Trig Functions • The 3 inverse trig functions (other 3 are reciprocals): • 1) • 2) • 3)

  5. Domain an Range • To make these functions, we need to restrict the domain and range DomainRange [-1, 1] [-1, 1]

  6. Evaluating Inverse Trig Functions • When evaluating these functions, we want to find the angle that results in the value. • Note: because of the restriction in the ranges, we can only consider angles in each range

  7. ex • Find each of the following function values • 1) • 2) • 3)

  8. Calculators • Calculators can be used to find inverse trig values • Inverse sin,cos,tan – buttons • Inverse reciprocals – your input will be the reciprocal

  9. Ex • Approximate using a calculator • 1) • 2) • 3)

  10. Closure • Evaluate in radians and degrees • HW: p.575 #1-35 odds

  11. 6.4 Inverse Trig FunctionsDay 2 • Do Now • Evaluate in radians and degrees • 1) • 2)

  12. HW Review: p.575 #1-35

  13. Composition of Trig and Inverse Functions • When evaluating a composition of trig and inverse trig values, compute the ‘inside’ first. • Keep in mind the domain and range of each composition

  14. Ex1 • Simplify

  15. Ex2 • Simplify

  16. Ex3 • Simplify

  17. Ex4 • Simplify

  18. Ex5 • Simplify

  19. Ex6 • Simplify

  20. Simplifying Compositions with X • When simplifying a composition with a variable, draw a right triangle with an angle that has the given ratio

  21. Ex • Find

  22. Ex • Evaluate

  23. Closure • Evaluate • HW: p.575 #37-67 odds

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