4. State the domain and the range of the cosine function.

5. ROLLER COASTER Part of a roller coaster track is a sinusoidal function. The high and low points are separated by 150 feet horizontally and 82 feet vertically as shown. The low point is 6 feet above the ground. 82 ft 6 ft 150 ft a. Write a sinusoidal function that models the distance the roller coaster track is above the ground at a given horizontal distance x. b. Point A is 40 feet to the right of the y-axis. How far above the ground is the track at point A?

4. A lighthouse is located 40 meters off-shore. The beam of light from the lighthouse rotates at a rate of 2 revolutions per minute clockwise. The beam hits a cliff on the beach 60 meters away, producing a dot of light that moves horizontally along this cliff. Let be the angle between the beam and the line through the searchlight perpendicular to the cliff. Use a trig function for the relationship. T a. How fast is this light moving along the beach when = if the beam is moving toward the h 3 perpendicular line? (remember you need radians for trig functions and their derivatives) b. How fast is this beam moving when I if the dot is moving away from the perpendicular 13 line? (Adjust picture to have light beam on other side of the vertical) beach/cliff CALCECCO 60m Lighthouse

Consider the function y = –4 cos (2x-5pi/3)-2 1. Describe the vertical translation. 2. Graph the function over exactly two cycles.

4T and x = 4т. Sketch the graph of the following between x = sin x 0.5+ 27 47 -Зл -27 -0.5- Draw: M Clear All

3. What is the amplitude of the graph y = -4sin (x - 2)? The amplitude is units. 2 4

Find the domain of the following function. f(x.y) = sin Select the correct choice below and fill in any answer boxes within your choice. O A. {(x.y): y +} (Use a comma to separate answers as needed.) O B. {(x.y): x+ and y+} (Use a comma to separate answers as needed.) OC. (x,y): x+ (Use a comma to separate answers as needed.) O D. R?

Graph the function. 1. y = 3 sin 2x + 2

Use the graphing utility to plot the graphs of y = cos (x) and y = 2x. (Enter multiple functions of x as a comma-separated list.) y = y 3. 2- -4 -3 -2 -1 4 3. 2- 4) 1.

5. Given the function y=-3sin| 2xr- + 8 , determine the following: Rewrite equation: amplitude: period: horizontal shift: vertical translation: Any reflections? If so, describe the reflection