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Name Review Chapter 9 - Graphing, Inverse Trig Functions and Solving Trig Equations 1. Determine an equation for each of the trig graphs shown below. a. d. b. c. e. 2. In the interval, 0 < < 2, graph y = 2cos½ and y = tan. State the number of times 2cos½ = tan. State TWO of the points of intersection of the two graphs. If necessary, round the coordiantes of the point(s) of intersection to the nearest thousandth. 3. State the amplitiude, frequency, period, and the range of y = -5sin( ¼x) + 9. 4. On the grid provided, graph one period of y = 3sin2. 5. In the interval 0 < < 2, graph the equation y = 4sin( - ). Write an alternate equation to represent the graph. 6. State all value of arcsin ( ½ ) such that 0 < θ < 360. 7. Evaluate: cos (arcsin 6/7) 8. In the interval –π < < , graph the equation y = - 3cosx + 5. 9. Evaluate and express your answer in radians: a. Arcsin (- ½ ) b. Arccos( - 3) 2 10. In the interval 0 < < 2, graph the equation y = 2sec 11. A small toy attached to the end of a slinky (or spring) goes up and down according to an equation of the form y = a sin(bx). The motion of the toy starts at rest, goes up to its highest position of 5 inches above its rest point, bounces down to its lowest position of 5 inches below its rest point, and then bounces back to its starting place in a total of 4 seconds. Write an equation that represents this motion. Graph your equation from x = 0 seconds to x = 12 seconds. 12. State the amplitiude, frequency, period, domain and range of y = 2sin(4x) – 5. 13. In the interval – < < , graph y = 3csc. 14. Evaluate, in terms of x: cos(arctan 4 ) 3x 15. Solve for all values of θ, such that 0 ≤ θ ≤ 360 - round to the nearest tenth of a degree when necessary. 8sin2θ - 5 = sin2θ - 2 16. Solve for all values of θ, such that 0 ≤ θ ≤ 360 – round to the nearest degree when necessary. 5sin2θ – 7cosθ + 1 = 0 17. Solve for all values of θ, to the nearest hundredth of a degree, such that 0 ≤ θ ≤ 360. 2cos2θ – 3sinθ = 1 18. Solve for all values of θ, to the nearest thousandth of a degree, such that 0 ≤ θ ≤ 360. 5 = 4cos2θ + 2 19. Solve for all values of x such that 0 ≤ x ≤ 2π. 3cosx + sin 2x = 0 20. The horizontal distance, in feet, that a golf ball travels when hit can be determined by the formula d = v2sin2θ g where v equals initial velocity, in feet per second; g equals acceleration due to gravity, θ equals the initial angle, in degrees, that the path of the ball makes with the ground; and d equals the horizontal distance, in feet, that the ball will travel. A golfer hits the ball with an initial velocity of 180 feet per second and it travels a distance of 840 feet. If g = 32 feet per second per second, what is the smallest initial angle the path of the ball makes with the ground, to the nearest degree?