Tuesday's Slides 4/24/07

Today we revisited inverse trig functions. Of particular importance were the domain and range of the inverse sine and the inverse cosine functions. Sine and inverse sine are inverses only if we restrict the domain of sine to [-pi/2, pi/2]. Otherwise, the inverse sine function would fail the vertical line test. Having thus restricted the domain of sine, the range of inverse sine is also restricted to [-pi/2, pi/2]. The domain of the inverse sine function is simply the range of the sine: [-1,1].

Remember with inverse functions:

• D-->R
• R-->D

Likewise, the cosine & inverse cosine functions are inverses only over the interval [0, pi], therefore the range of the inverse cosine function is also [0, pi]. See slides 1 & 2 for a graphical interpretation.

Next we started a problem involving the derivative of an inverse trig function (see slide 3). We did not solve the problem as we do not yet know how to differentiate the inverse tangent function. We did derive the derivative formula for the inverse sine function (slide 4). The derivation process is a little hard to think of but is algebraically pretty straight forward. The key is rewriting the inverse trig equation as the corresponding trig equation.


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Tomorrow, we will derive the derivative formulas for the other inverse trig functions & then finish the batter problem.


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