Section 3.10 Activity - Inverse Trigonometric Functions and Their Derivatives 1. Find the exact value of each of the following: (a) tan cos" (b) sin 2 tan- 2. Simplify each expression. (a) cos tan ' (Vx)) (b) tan 2 cos (x4 )) 3. Find each derivative. 3 -x (a) dx arctan V3+x (b ) wasin ' ( w' ) - cos- (w) )5. Find each derivative: (a) [sec-' (Inx) ] 6. Losc" (3k + 2) ]4. The function H(t) = 221sin 1-7+221 models a person's height in feet from the bottom of the London Eye Ferris wheel after boarding at the bottom and traveling around the wheel for t minutes. (a) Graph H(t) in the plane below. (b) Determine an appropriate interval for t so that 425 .y=H(1) H (t) is one-to-one. 400 375- 350 -325- -300 - -275+ (c) Find H (t) . 250 - "225- 200- 175 -150 - 125- 100- -75- ". 25+ K- (d) Find " ( H(1) ) and A ( H-' (1 )). (e) What are the units of " (H(t)) and " (H ' (1)) . (f) Assume that the Ferris Wheel operates for 30 minute time intervals. Over one such time interval, at what values of t does the rider reach the maximum height