More Inverse trig functions

1. More Inverse trig functions

2. Find the derivative of y = cos-1 x cos y = x Take the cosine of both sides cos is adj/hyp so adj = x and hyp =1 so side opp is 1-x2 so the sin y = 1-x2 -sin y y’ = 1 y’ = 1/-sin y which means that y’ = 1 / -1 – x2

3. Find the derivative of y = tan-1 x on your own. tan y = x Take the tangent of both sides tan is opp/adj so opp = x and adj =1 so hyp is 1 + x2 so the sec y = 1 /1 + x^2 Sec2y y’ = 1 y’ = 1/sec^2y which means that y’ = 1 / 1 +x^2

4. Find the derivative of: a) y = sin-1 4x b) y = tan-1 x3 c) y = (cos-1x/2)3 d) y = x sin-1 x + 1 – x2

5. An officer in a patrol car sitting 100 feet from the highway observes a truck approaching. At a particular instant of t seconds, the truck is x feet down the road. The line of sight to the truck makes an angle of  radians to a perpendicular line to the road. Express  as an inverse trig function

6. An officer in a patrol car sitting 100 feet from the highway observes a truck approaching. At a particular instant of t seconds, the truck is x feet down the road. The line of sight to the truck makes an angle of  radians to a perpendicular line to the road. b) Find d/dt

7. An officer in a patrol car sitting 100 feet from the highway observes a truck approaching. At a particular instant of t seconds, the truck is x feet down the road. The line of sight to the truck makes an angle of  radians to a perpendicular line to the road. c) When the truck is x = 500 ft, the angle is observed to be changing at a rate of -2 degrees/sec. How fast is the car going in ft/sec and mph?

8. Find the integral of each of the following. 1) dx/1 – x^2 2) dx/4 – x^2 3) dx/1 + x^2 4) dx/2 + 9x^2

9. Find the integral of each of the following. 5) dx/5 – 2x^2 6) e^x/9 + e^xdx 7) x + 2/4 - x^2dx 8) x + 2/x^2 + 4dx