Please explain and show steps

1. Solve the following equation for all x in [0,27): 2 sin (x) + 9 sin?(x) = 5 sin(x). Your answer should include algebraic steps in solving the equation as well as pictures/graphs demonstrating how you found x. [5] 2. Create an application problem (real-world, but doesn't have to be that real) that uses "the ambiguous case" of the Sine Law. Solve your problem with explanations where necessary. [4] 3. A cottage is built near the coast of an ocean on a different planet. just like on Earth, the coast has tides that go in and out, however they are not on the same 24-hour cycle as on Earth. On average, the water reaches 20 metres away from the cottage, but at high-tide the water reaches a shed that is only 12 metres away from the cottage (and directly between the cottage and the ocean). On January 1st (on Earth) The water's edge is at the 20-metre mark at 8am and 6pm (in Earth time). At 8am the water's edge is approaching the house and at 6pm it is receding. We can describe the distance between the water's edge and the cottage as a function D(t) (in metres), where t is the number of hours after midnight on January 1st. a) Explain why we would use a sine or cosine function for the function D (t). [1] b) Find the period and amplitude of D(t). Provide brief explanations about the calculations and the relevance of the numbers you've chosen. [2] c) Sketch the graph of D(t) with at least two periods. [1] d) Find a formula for D(t). [2]