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Inverse Trig Functions

Inverse Trig Functions. Section 4.7 . Inverse Sine, Cosine, Tangent Functions. and it’s inverse. y = sin x. y = arcsin x. EXAMPLES. OR. EXAMPLES. Q: How do we explain the inconsistency??. A: It’s a matter of Domain and Range. y = cos x. y = arccos x. EXAMPLES. OR. EXAMPLES.

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Inverse Trig Functions

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  1. Inverse Trig Functions Section 4.7

  2. Inverse Sine, Cosine, Tangent Functions and it’s inverse

  3. y = sin x y = arcsin x

  4. EXAMPLES OR

  5. EXAMPLES Q: How do we explain the inconsistency?? A: It’s a matter of Domain and Range

  6. y = cos x y = arccos x

  7. EXAMPLES OR

  8. EXAMPLES Q: How do we explain the inconsistency?? A: It’s a matter of Domain and Range

  9. y = tan x y = arctan x

  10. EXAMPLES Q: How do we explain the inconsistency?? A: It’s a matter of Domain and Range

  11. Let’s talk DOMAIN and RANGE…

  12. Let’s talk DOMAIN and RANGE…

  13. Let’s talk DOMAIN and RANGE…

  14. Now some examples…Evaluate w/out Calc Find the cosine of the angle whose sine is ½ Start with innermost expression Work your way out Evaluate

  15. Now some examples…Evaluate w/out Calc Find the angle whose sine is the cosine of Start with innermost expression Work your way out Evaluate

  16. Now some examples…Evaluate w/out Calc Find the angle whose cos is the tangent of Start with innermost expression Work your way out Evaluate

  17. Example: #41 & #42*, P. 422

  18. State the DOMAIN and RANGE the composite function Decide the domain of innermost function This is your DOMAIN Find RANGE of innermost function This is the DOMAIN of the outer function Determine the RANGE based on “new” DOMAIN

  19. State the DOMAIN and RANGE the composite function Decide the domain of innermost function This is your DOMAIN Find RANGE of innermost function This is the DOMAIN of the outer function Determine the RANGE based on “new” DOMAIN

  20. State the DOMAIN and RANGE the composite function

  21. Angle whose tan is x =

  22. #25, p. 433: A boat is due east of the shoreline running north/south. The bearings of the boat from two points on the shore that are 550’ apart from each other are 100 and 110 degrees. How far is the boat from the shore? x Consider two of the triangles formed in the diagram.

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