1-

b) Use a graphing utility to graph the functions f(x) = 2 cos(2x) + 4 sin(7x) and g(x) = 2 cos(2x) + 4 sin(4x). Use the graphs to find the period of each function. period of f(X) period of g(x) Is the function h(X) = A cos(ax) + B sin(,8x), where a and ,8 are positive integers, periodic? Explain. 0 Yes, h(x] is periodic because each of its terms is periodic and a common multiple of their periods can be found. 0 Yes, h(X) is periodic because each of its terms is periodic with the same period for all values of a: and B. O No, h(x) is not periodic unless A = B. O No, h(x) is not periodic unless A and B are also positive integers. O No, h(x) is not periodic unless a: = ,8. Two trigonometric functions f and g have periods of 3, and their graphs intersect at x = 6.55. (a) Give one positive value of x less than 6.55 and one value of x greater than 6.55 at which the functions have the same value. less than 6.55 X = greater than 6.55 X = (b) Determine one negative value of x at which the graphs intersect. X = (c) Is it true that f(18.55) = g(-8.45)? Explain. O Yes. Both 18.55 and -8.45 are a whole number of periods away from the given point at which the graphs of f and g intersect. O Yes. The value 18.55 is a whole number of periods away from -8.45, which is all that is necessary to guarantee that f(18.55) = g(-8.45). O No. Since 18.55 # -8.45, f(18.55) # g(-8.45). O No. The value 18.55 is not a whole number of periods away from the given point at which the graphs of f and g intersect. O No. The value -8.45 is not a whole number of periods away from the given point at which the graphs of f and g intersect.(a) While standing in water that is 2 feet deep, you look at a rock at angle .9 = 50 (measured from a line perpendicular to the surface of the water). Find 62 in degrees. 1 (Round your answer to one decimal place.) (b) Find the distances x and y, in feet. (Round your answers to two decimal places.) \"SH \"SH (c) Find the distance d (in ft) between where the rock is and where it appears to be. (Round your answer to two decimal places.) (d) What happens to d as you move closer to the rock? Explain. Q As you move closer to the rock, (1 must get larger and larger. The angles .91 and .92 will decrease as the distance y increases, so d will increase. 0 As you move closer to the rock, d must get smaller and smaller. The angles 61 and 62 will decrease along with the distance y, so 0' will decrease. 0 As you move closer to the rock, d must get larger and larger. The angles 6'1 and 6'2 will increase along with the distance y, so C! will increase. 0 As you move closer to the rock, d must get smaller and smaller. The angles 61 and 62 will increase as the distance y decreases, so 0' will decrease. 0 As you move closer to the rock, d does not change. The angles 61 and 62 will remain the same along with the distance y, so of will also remain the same.