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name: Mathematics 142 first test Wednesday, April 22, 2009 please show your work to get full credit 1. Convert 3π radians to degrees. 10 2. An central angle of 28◦ intercepts an arc of a circle of radius 400 centimeters. (a) Find the radian measure of the angle. (b) Find the length of the intercepted arc. 3. The terminal side of angle A in standard position intersects the unit circle at the point (x, y) = −12 5 , 13 13 Write down the values of the six trigonometric functions of A. 4. The inverse trigonometric equation cos−1 n = A is equivalent to the trigonometric equation 5. Find the exact value of cos , with angle restriction ≤A≤ 5π (Your answer should involve square roots. Don’t give a decimal approximation) 6 page two 6. How many solutions does each of the following equations have? (It is not necessary to write down the solutions) (a) cos A = 3 4 (b) csc θ = 3 7. Find all the solutions of √ sin θ = − 2 2 9. Use a calculator to estimate the value of (a) cot π 5 (b) sec−1 (−2) (c) tan−1 x = π 3 (d) sin−1 x = π 8. Find all the solutions between 0 and 2π of π 1 = cos θ − 4 4 3 10. Find the exact value of tan cos−1 10 page three 11. True or False ? (a) cos(−A) = − cos A (c) cot 90◦ is undefined (b) tan(A + π) = − tan A 30 20 − 5π , 0 12 10 0 19π , 0 12 ‐10 ‐20 ‐30 12. For the sinusoidal graph shown above (a) State the amplitude: (b) What is the period? (c) Find an equation for the graph in the format y = A sin(ωx − C) page four 13. Sketch a graph of y = 80 cos (30x) Be sure your graph includes the exact location of all quarter-cycle points. 14. Specify the locations of the vertical asymptotes to the graph of f (x) = tan x 60