page+17


 * Aim: How do we sketch the graphs of the inverses of the sine, cosine, and tangent functions?**

For this lesson we need to remember one thing: when dealing with the inverse of any function we have to remember it is reflected in the line y=x. If we know the values for sin, cos and tan all we need to do is switch the domain with the range. We will then have the points for the inverse function.

We have to remember that in order for a function to have an inverse: 1. it must be a function (vertical line test) 2. it must be one-to-one (horizontal test)

Sometimes we will have to restrict the domain so that we will get one-to-one. When we graph a whole period of a trig function it may not be one-to-one.

Also, when we are done, the domain will become the range and the range will become the domain.

[|video]

We label the inverse functions as cos^-1, sin^-1 o tan^-1. Or we can just call them arccosine, arcsine, or arctangent. All this means is what is the value of the angle that gives us a certain value. Example: y=arccos(1/2). This means what is the angle whose cosine is 1/2. That answer is 60 degrees.

Try some of your own: Do #3-35 odd

[|Inverse_Angles.JPG]

Answers

[|A-Inverse_angles.JPG]


 * Journal entry:** Explain why sometimes we have to restrict the domain of an inverse function.