quizzes 5-7

Quiz 5 MATH 115 Fall 2019 SHOW ALL WORK to receive credit. Problems 1-2. Use a calculator to find the function values, accurate to four decimal places. 1. 1 pt. sec 246° 2. 1 pt. tan(-5π/9) 3. 2 pts. Find this value exactly: arcsin [cos(11π/4)]. Finding an “exact value” means that decimal approximations from a calculator are not acceptable as answers. Problem 4. 4 pts. Prove the identity. Use algebra and basic trigonometric formulas to transform one side of the equation to look like the other side. Show the whole process, without skipping any steps, and explain what you are doing in each step. Use specific explanations, and not vague descriptions such as “Simplified.” (4 points = algebraically correct proof, with all steps included, and explanations provided for each step. 2 points = Proof missing steps, but algebraically correct and explanations provided for each step. 0 points = Algebra is not correct and/or explanations are not provided for each step.)

1

5. Given cosα = 3/4 with 3π/2 < α < 2π, and tanβ = -1 with π/2 < β < π. Find the exact values for the following (no decimal approximations). Simplify your answers. A. 2 pts. Find cot α B. 3 pts. Find sin(2β) C. 3 pts. Find cos(α - β)

D. 3 pts. Find tan(α/2)

Problem 6. 3 pts. Solve, finding ALL solutions. Express your answer in radians, with exact values.

Solve

7. 8 pts. For the function

A. Graph at least one period of the function. Be sure to label the scales on your axes. B. Find the amplitude, period, and phase shift. C. Find an ordered pair for a point on the graph of the function, where x is 3π/2. Find exact values. D. Find an ordered pair for a point on the graph of the function where y is 0. Find exact values. Answers: B. The amplitude is __________ The period is ___________ The phase shift is ________ C. The point on the graph is: (3π/2, _______). D. The point on the graph is: (__________, 0).