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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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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
Trig functions also have inverses Function: Inverse
How Trig Inverses Work The work in the “opposite” direction of a trig function So the inverse will be So the inverse will be
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
Example 1 from the Circle Reference angle is and sin-1 is defined in Quadrants I and IV so the answer will be
Example 2 from the Circle Reference angle is and cos-1 is defined in Quadrants I and II so the answer will be
Example 3 from the Circle Reference angle is and Tan-1 is defined in Quadrants I and IV so the answer will be
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
Combination Example 1(without a calculator) Draw a triangle based on Arcsin 3 2 Write the answer of Cos from the triangle
Draw a triangle based on Arccos 7 Write the answer of Tan from the triangle
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
Sum and Difference Formulasfor Sine & CosineChapter 7 Section 4
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
The Identity for Cosine is also unusual. Important: If you are adding, the result is Subtracted If you are subtracting, the result is Added
This is the pattern for Sine and we will be using Subtraction