Which of the following best corresponds to the x-value where the function f(x) = cosx is a minimum in the interval x = [25, 30]? O A. 25.1 O B. 26.7 O C. 28.3 O D. 29.8Which of the following functions has a local maximum at x = IT? O A. sin x O B. COS X O C. tan x O D. CSC X O E. sec x O F. cot xWhich of the following pairs of functions have identical domains? O A. tan x and csc x O B. tan x and sec x O C. tan x and cot x O D. csc x and sec x O E. sec x and cot xWhich of the following functions is even and has asymptotes at x = - + kx , where k is an integer? O A. sin x O B. COS X O C. tan x O D. CSC X O E. sec x O F. cot xAweight is suspended from a spring and allowed to hang at its rest position. It is then pulled down 2 in., released. and allowed to oscillate up and down. Its location [in inches) relative to its rest position is given by the function f0) . J sin[2.5r - a , where t is the time in seconds. How much time will it take for the weight to move through one complete cycle of motion? 0 A. 2.5 seconds 0 B. 3.1 seconds 0 C. 3.8 seconds 0 D. 5.0 seconds Consider the function f(x) = asin( ex + c) . Which of the following combinations of parameter values will result in a graph of f(x) identical to that of the parent function, sin x? O A. am-1, b- 1, cuz O B. a =-; b = 2; c =0 O C. a=1; b--1,c- O D. a=1; b=-1; c = *A trigonometric function with no asymptotes oscillates between the values of y= -4 and y = 0. Two consecutive zeroes are located at approximate x-values of 3.48 and 7.66. Which of the following best represents the equation of the trigonometric function? O A. f(x) =-2sin (-1.5x+0.5)-2 O B. f(x)= -2sin(1.5x+ 0.5) - 2 O C. f(x) = 2sin(-1.5x+0.5) - 2 O D. f(x) = 2sin(1.5x + 0.5) -2At time t = 0 seconds, a clock pendulum makes its maximum angle with the vertical, reaching a positive angle of 6". In one minute, the pendulum swings back and forth 20 times. Which of the following best expresses the angle the pendulum makes with the vertical in degrees as a function of time in seconds? O A. e(t) - 6cost O B. e(t) =6cost O C. a(t ) - 6sing O D. a(t ) = 6sin 25 ,)Over which of the following domains is f( x) = csc(0.1x +1.2) defined at all points and invertible? O A. x= [0,10] O B. x= [10, 20 ] O C. x=[20, 30 ] O D. x= [30,40 ]Using the standard restricted domain for the cotangent function, which of the following best describes the behavior of the inverse cotangent function? O A. a decreasing function defined in Quadrants I and II O B. a decreasing function defined in Quadrants Ill and IV O C. an increasing function defined in Quadrants I and II O D. an increasing function defined in Quadrants Ill and IVWhich of the following best represents the value of arcsec 1.6 in degrees. using the standard restricted domain? 0 A. 39 0 B. 51 0 C. 78 0 D. 129" Using the standard domain for the sine function. which of the following expressions eorresponds to the composite function sin[mosx)? O A. O B. m m Gem 1)? our Given the standard restricted domains, which of the following relationships does not hold for x - -1? (Assume angles are in radians.) O A. sin ( arcsin x) = x O B. arcsin (sin x) = x O C. cos( arccosx) = x O D. arccos (cosx) = x O E. tan ( arctan x) = x O F. arctan ( tan x) = xThe slope of the minute hand on an analog clock is given by the expression cot 30 , where t is time in minutes. Which of the following best represents the first time when the slope is 0.5? O A. 9.7 mins. O B. 10.0 mins. O C. 10.3 mins. O D. 10.6 mins