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Practice Questions: 1. a) Determine the exact value of: cos 12 2. Given sin x following: a) b) Determine an expression that is equivalent to: 7 sin 6 5 3 3 x 2 , determine the exact values for the , 0 x and cos y , 13 2 7 2 cos 2x b) sin x y c)sin2x d) tan 2x 3. a) Solve. Determine exact solutions when possible and approximate solutions otherwise. 2 cos 2 x 5 cos x 3 b) c) 5 sin x 3 3 sin x cot x 2.8 4. Prove. sec x sin x 2 tan x csc x cos x a) c) b) tan 2 x cos 2 x 1 1 cos 2 x 2 cos x sin 2 x 2 csc 2 x tan x 1 cos 2 x 5. The population of a ski resort town, as a function of the number of months into a year, can be described by a cosine function. The maximum population of the town is about 15 000 people, and the minimum population of the town is about 500 people. At the beginning of the year, the population is at it’s greatest. After 6 months the population reaches its lowest number of people. a) What is the equation of the cosine function that describes the population of this town? b) Use the function to find the time(s) at which the population will be 4000. 6. 3 x Simplify sin x cos x tan x tan 2 2 2 7. Prove. a) cosx y cosx y cos2 x cos 2 y 1 8. Find all solutions in the interval 0 x 2 : b) log 10 csc x log 10 sin x a) cos 2x sin x 1 b) sin 2x sin x cos x 0 9. The paddle wheel of a steamboat is 22 feet in diameter and is turning at 3 revolutions per minute. The axle of the wheel is 8 feet above the surface of the water. Assume that a point P on the edge of the paddle wheel is at 0,19 at time t 0 seconds. a) b) c) d) e) 10. 11. What maximum height above the water does point P reach? How far below the water does point P reach? In how many seconds does the wheel complete one revolution? Write a cosine function for the height of point P at time t. Use the function from part d above to find the time(s) at which point P will be at a height of 10 feet. State the degree and radian measure of an angle in standard 7 position formed by rotating the terminal side by of a circle. 12 7 Convert to degrees. 15 ____________ ____________ 12. Convert 252 to radians. Write your answer in terms of . ____________ 13. State the radian measure of one positive and one negative angle in 7 standard position that are co-terminal with in standard position. 5 ____________ 14.Determine the length of the circular arc with a central angle of 2 radians. Assume that the circle has diameter 10. ____________ ____________ 15. P (33,56) determines an angle in standard position. Determine all six trigonometric ratios of angle . 16. State the exact value of each of the following. a) cos 5 3 ____________ b) csc 7 4 ____________ 17. 18. 19. 2 Write cos 3 2 cos sin 3 sin as a single real number. For y sec , a) Determine the location of any vertical asymptotes. b) Sketch the graph for 2 2 . c) state the domain and range For y cos X y 4 cos3x 1 a) Sketch the graphs for 2 2 . b) State the length of the period. c) state the range for each graph. ____________