Unit #5: Deriving Trigonometric Functions Assignment 1. Differentiate with respect to r. (a) (1 point) f(x) = 2 sinc (b) (2 points) g(x) = -5x + Vx- COST 2. (4 points) Find the exact equation of the tangent to y = 3 sinx at a = 3. Find s dy for each of the following. dx (a) (2 points) y = sin(x - 2) (b) (3 points) y = x2 cos(x2 - 2x + 1)In the Iron Islands, the tides cause the water level to rise above 4 m above average sea level and to drop to 4 In below average sea level. One cycle is completed approximately every 8 hours. The changes in the water depth can be modeled by a sinusoidal function. (a) (2 points) Determine a function to model this situation. At midnight {t = 0) the water is at low tide. (b) (3 points) Determine the rate of change of the water at 13:45 pm. The movement of the waterwheei in Riverrun can be modelled by the function Mt) : 13cos (%t) + 12. (a) (2 points) Determine a function describing the velocity of the waterwheel as a function of time. (b) (4 points) Determine the point (5) at which the height is changing the fastest. What is the velocity at this time