(1) Suppose that sins: : % and g

(I) Suppose that sinx and < .T < T. (a) Determine the value of cos:r. (b) Determine the values of tan:r, cot:r, sec:r, and csc:r. (2) Sketch the graph of f(:r) 3sin(4x 2). (3) Suppose that the displacement from equilibrium of a damped harmonic oscil- lator is given by :r(t) (a) Determine the period and frequency of the oscillator. (b) Determine the amplitude of the oscillator as a fimction of t. (c) Sketch the graph of as a function of t. Be sure to indicate the envelope. (4) Find all solutions of the equation sin (5) Consider the equation tan(3:r -F I) 2. (a) Sketch the graphs of y tan(3:r -F I) and y 2 on the same plane. (b) Find one solution of the equation. Give its exact value and a decimal approximation with three decimal places. (c) Find all solutions of the equation. You only need to give their exact values.