Today we continued exploring the derivatives of inverse trig functions.
The 1st two slides show problems that require the use of the chain rule and the derivative of the inverse sine function.
We then returned to the derivation of the derivative formula for the inverse sine function. During the derivation we ignored the +/- square root when solving for cosy. We must ignore the negative root because the inverse sine function is increasing over the entire domain. A negative root would imply a negative slope to the curve and this is not the case over the domain [-1,1].
We then derived the formula for d/dx(inv cosx) and d/dx(inv tan x). (see the slides for the formulae)
Lastly we returned to the batter problem of yesterday and finished it. The batter would need to track at 65 radians/sec to keep his or her eye on the ball. Mr. A. reported that scientists estimate a limit of 3 radians/sec as the maximum rate at which humans can track a moving object. The last slide addresses this limit.
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Homework: Page 542 17-31 odd, 45
Keep working on your final project.
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