4.7 Inverse Trig Functions

Does the Sine function have an inverse? 1

What could we restrict the domain to so that the sine function does have an inverse? 1

Inverse Sine,, arcsine (x) Function is increasing Takes on full range of values Function is 1-1 Domain: Range:

Evaluate: arcSin Asking the sine of what angle is

Find the following: a)ArcSin b) c) ArcSin

Inverse Cosine Function What can we restrict the domain of the cosine curve to so that it is 1-1? 1

Inverse Cosine,, arcCos (x) Function is increasing Takes on full range of values Function is 1-1 Domain: Range:

Evaluate: ArcCos (-1) The Cosine of what angle is -1?

Evaluate the following: a) b)ArcCos c)

ArcTan (x) Similar to the ArcSin (x) Domain of Tan Function: Range of Tan Function:

arcCos (0.28) Is the value 0.28 on either triangle or curve? Use your calculator: –

Determine the missing Coordinate

Use an inverse trig function to write θ as a function of x. θ 2x x + 3

Find the exact value of the expression. Sin [ ArcCos ]

4.7 Inverse Trig Functions

So far we have: 1)Restricted the domain of trig functions to find their inverse 2)Evaluated inverse trig functions for exact values 3)Found missing coordinates on the graphs of inverses 4)Found the exact values of compositions

Composition of Functions 1)Evaluate innermost function first 2)Substitute in that value 3)Evaluate outermost function

Sin (arcCos ) Evaluate the innermost function first: arcCos ½ = Substitute that value in original problem

How do we evaluate this? Let θ equal what is in parentheses

θ

How do we evaluate this? Let θ equal what is in parentheses Use the triangle to answer the question θ

What is different about this problem? Is 0.2 in the domain of the arcSin?

What is different about this problem?

Graph of the ArcSin YX = Sin Y

Graph of the ArcSin

Graph of ArcCos YX = Sin Y

Graph of the ArcCos