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name: Mathematics 120 test four Monday, December 6, 2004 please show your work to get full credit for each problem no calculators on this test 2π radians to degrees. 3 1. Find the reference angle of 215◦ . 2. Convert 3. Find two other angles which share a terminal side with the angle −45◦ . 4. A central angle θ in a unit circle intercepts an arc of length 2. Find the radian measure of the angle θ. s=2 θ r=1 5. An central angle of 20◦ sits in a circle of radius 4000. What is the length of the intercepted arc? 20° r=400 s=? 6. The equation sin−1 n = θ is equivalent to the statement where ≤θ≤ page two 7. Evaluate each of the following quantities: (a) sin (e) sin π 3 −1 (b) cos 1 2 3π 4 −1 (f) cos (c) tan (−30◦ ) √ ! 3 − 2 2 (g) tan arccos 3 (d) sec 8. Sketch a graph of 1 π x− . 30 3 The sketch should include the exact location of all quarter-cycle points. y = 20 cos 2π 3 page three y 50 x -.01 .02 .05 .08 .11 -50 9. Given the graph of a modified sine graph above, find each of the following: (a) amplitude = (b) period = (c) frequency = (d) shift = (e) equation of this graph: 10. Find two angles between 0 and 360◦ which solve each of the following equations: (refer to the unit circle diagram) (a) cos θ = 0.2 (b) sin θ = −0.4 (c) tan θ = −1 page four 11. Solve each of the following triangles for the indicated quantities: (a) 400 y 1 (b) θ 60° 3 x (c) L 45° 8 30° x