Test 3 Online Extended Response NAME: 1. (5 points) Find all values of 0 and all values of 0 in [0, 27] for the equation given below. Be sure to the algebra or trigonometry you use and give exact values to ensure full credit. cos(3x) = V3 2. (5 points) Use sum/difference formulas for sine and cosine to prove the identity below. Prove the identity below by starting from the left side and ending with the right side of the equation. Be sure to show the algebra and trigonometry you use and give exact values to ensure full credit. sin ( 1 - 4 ) - cos ( 2 - 7 ) = -VZ3. (10 points) Use the function defined below to answer (a) through (g). f(x) = 2sin(x) +1 (a) What is the period? The period is (b) What is the horizontal shift? The horizontal shift is (c) What is the vertical shift? The vertical shift is (d) Show your work to find the x-intercepts over the interval [0, 2x]. Be sure to include the equation 2sin(x) + 1 = 0 in your answer. (e) Show your work to find the y-intercept. Be sure to include an equation with f(0) in your answer. (f) Sketch the graph over the interval [0. 27]. Be sure to label all intercepts with exact values. (g) What is the domain and range for the function. Give your answer in interval notation. Domain: Range