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2412 Chapter 7 Sections 1-4

2412 Chapter 7 Sections 1-4. Inverse functions in general. An inverse function does the “opposite” of the original function. Examples include:. Function: Inverse. Inverse of radical. Inverse of subtraction. Inverses are used in solving equations.

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2412 Chapter 7 Sections 1-4

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  1. 2412 Chapter 7Sections 1-4

  2. Inverse functions in general An inverse function does the “opposite” of the original function. Examples include: Function: Inverse

  3. Inverse of radical Inverse of subtraction Inverses are used in solving equations

  4. Trig functions also have inverses Function: Inverse

  5. How Trig Inverses Work The work in the “opposite” direction of a trig function So the inverse will be So the inverse will be

  6. Restrictions on Inverse Functions Since Trig values repeat going around the circle, we restrict some inverse functions so we only get one answer (calculators do this automatically) Domain Restrictions Range Restrictions Arcsin -1 < x < 1 I and IV Arccos -1 < x < 1 I and II Arctan Any Value I and IV

  7. Example 1 from the Circle Reference angle is and sin-1 is defined in Quadrants I and IV so the answer will be

  8. Example 2 from the Circle Reference angle is and cos-1 is defined in Quadrants I and II so the answer will be

  9. Example 3 from the Circle Reference angle is and Tan-1 is defined in Quadrants I and IV so the answer will be

  10. Calculator ExamplesType: 2nd Sin, 2nd Cos , 2nd Tan This doesn’t exist because sin-1 x is restricted -1 < x < 1 .6435 radians or 36.8699º -1.5658 radians or -89.7135º

  11. Combination Example 1(without a calculator) Draw a triangle based on Arcsin 3 2 Write the answer of Cos from the triangle

  12. Draw a triangle based on Arccos 7 Write the answer of Tan from the triangle

  13. Draw a Triangle:

  14. Simple Inverse Equations

  15. Operations with Trig FunctionsChapter 7 Section 3

  16. Proving Identities(Work only on one side) Caution: You need to work the identity . . . Math Lab makes it easy by giving all of the steps

  17. Sum and Difference Formulasfor Sine & CosineChapter 7 Section 4

  18. There is a distributive property for Sine but it is not what you expect. Important: If you are adding, the result is added If you are subtracting, the result is subtracted

  19. Uses: Find angles related to those that we have memorized.

  20. The Identity for Cosine is also unusual. Important: If you are adding, the result is Subtracted If you are subtracting, the result is Added

  21. This is the pattern for Sine and we will be using Subtraction

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