Show all work. Please box your final answers. 1. Find first four solutions to 6 sin(3t) = 5. Give your answers EXACTLY. No credit will be given for decimal approximations. (4 points) 2. Suppose the depth of a particular pond (in inches) varies annual according to the function below, where t is the number of months since March 1. (For simplicity, assume all months are approximately the same length.) D(t) = 18 cos ( t) + 10 In the problems below, round all your answers to two decimal places, and include units. a. How deep is the pond on May 1? (2 point) b. We'd like to know the first time in the year when the pond drops to a depth of 10 inches. Set your function from part (a) equal to 10, and solve the equation for the trig function in it. Show all your work! What month and approximate day is this? Round your answer. (4 points)Math 142 Week 6 Activity. Be sure to show all your work, give EXACT answers unless otherwise noted, and box your answers. 10 points total. 1. Solve on [0,2x). All angles should be given in radians. Decimal answers will receive zero credit. (4 points) 5 sin(2x) = cos (x) 2. Prove the identity USING OUR REGULAR PROOF FORMAT. (Hint: start with left side.) (3 points) sin x + sin y cos x + cosy (( + x) 2 ) up- 3. If cos(x) = -= where x is in the second quadrant, find sin (2x). (3 points)