show work.

1. (10 pts) Solve the equation sin(2x) = v2 sin(x) , finding all solutions in the interval [0, 2n). (You should be able to provide the exact values of the solutions and state them in radians.) 2. (10 pts) Solve the equation 3 arccos(2x) = 2n.. 3. (10 pts) For the triangle ABC: we are given that C = 65, a = 16.0, and c = 24.0. (Side a is the side opposite angle A, side b is the side opposite angle B, and side c is the side opposite angle C.) Solve the remaining side. 4. (10 pts) The Pentagon in Washington D.C. is 921 feet long on each of the five exterior sides. $54 540 A 921 ft. B What is the distance from a vertex to the center of the Pentagon?. That is, what is the distance between A and C? 5. (60 pts 10 each) Let v = (3, 1) and w = (2, -4) (a) Find Su + 6w and state the result in component form. (b) State the exact magnitude (length) of v and the exact magnitude of w. (c) State the dot product D - w. (d) Find projw (v) in component form. Give exact values. (e) Sketch v and w (f) Determine the angle between v and w. .Write the exact angle as the arccosine of an appropriate number