All questions solution and explanation, handwritten.

1. Consider the equation 5 sin(nx + 1) + 3 = 0. a) Determine all possible solutions, to 2 decimal places. b) Solve for x E [0,6], to 2 decimal places. 3. A spring is pulled 32 cm from the wall and is let go. Its minimum distance from the wall is 8 cm and it takes 2 seconds to complete a full cycle. Neglecting friction, determine the times at which the spring is 12 cm from the wall in the first 10 seconds. 4. Solve the following equation for x E [-n, n]. 2 tan(2x - 1) - 1 = 6 2. A Ferris wheel with a diameter of 20 metres completes a one turn in 2 minutes. A passenger hops on at ground level for a 3 turn ride. Photos are taken when a cart is 16 metres above the ground and are made available for sale after the ride. Determine the times at which the camera should be set to snap pictures during a passenger's ride. Approximate answers to 1 decimal place. 5. Consider the Ferris wheel in (2). The nightly fireworks can be seen from a cart on the ride when the height of the cart is greater than 5 metres above the ground. Determine the times that that a rider can see the watch the fireworks during a ride