Complete all sections with all solutions handwritten & explanations

Section 1 Section 3 1. Solve 3 tan' x - tan x = 0 for exact values of x E [-2nt, 2x]. 1. The paddle wheel of a steamboat has a radius of 3 metres and goes 1 metre below the surface of the water. The wheel completes 15 revolutions per minute. If time is measured from the moment the paddle passes the sidebeam (" radians from the horizontal, moving toward the water), determine the times at which that paddle 2. Solve 2 sin x + 5 sin x - 3 = 0 for exact values is at water level in the first 30 seconds. of x E [-41, 47]. 3. Solve 4 cos?(4x) = 3 for exact values of x E [0,37]. 4. Solve the equation -25 sin ( x + 10) + 12 = 17 for x E [0,30]. 2. Determine the exact value of cos (sin-1 (- 5)). 5. The Acme Video Sharing Service, a successful start-up, has announced that it is interested in being bought out. Many companies are expected to express interest. Daily rumours have resulted in a fluctuation of the company's stock. Models for the month of April predict the stock value I to be given by the equation V(t) = -5 sin " (t + 1)|+ 13, with t in days. "Sell" recommendations are set to when the stock rises to 17$ and 3. Solve- = sin(2x) + cos(2x) on [-2n, 2n]. "Buy" recommendations are set to when the stock decreases to 17$. Determine the times in the first 15 days sin(2x)-cos(2x) of April when investors will be expected to buy and sell the stock. 4. The table of values below presents the average monthly populations of a winter resort village, which fluctuates throughout the year. Pay parking is enforced in the village when the population is above 5000. Section 2 Estimate the number of days per year that pay parking is enforced. 1. Solve 3 sin x = 1 + cos x for x E [-2n, 3x]. Month Population (thousands) January 10.5 February 9.3 March 7.8 2. Solve cos(2x) - 1 = 3 cos x. April 6.0 May 4.9 June 4.5 July 4.7 5.8 3. Solve 2 cos x csc x (1 - cos(2x)) = 1 August September 7.6 October 94 November 10.6 inn 4. The motion of a dolphin is modelled by the equation H = cosd + sin(2d), where H is the height of the dolphin, in metres, relative to the water level, and d is the horizontal distance travelled, also in metres. Determine the exact distances at which the dolphin is at water level in the first 10 metres horizontally