Question 1-11

Knowledge & Understanding: 1. Convert 5 radians into degrees: (a) 200 0 Mark Value: 3 (b 57 36 (d) 900 2. (e) -1 Determine the minimum of the trigonometric function f(x) = -2 cos(3x) -4 (f) -2 (8) -4 (h) - 6 Mark Value: 3 3. Convert 1.60 into radians: (1) 2x () 160n (k) 160 Mark Value: 3 4. Which equation represents the following function? (a) f(x) = tan x (b) f(x) = csc x (c) f(x) = sec x (d) f(x) = cot x Mark Value: 3 Thinking: 5. For what values of x is tan x undefined? Mark Value: 2 (i) x= m,nel () x= "tn,nel (k) x = n2x,nel (1) x = =+n21,nel 6. Which of the following pairs of functions have identical x-intercepts? (a) f(x) = sin x, f(x) = tan x (b) f(x) = cosx, f(x) = sin x (c) f(x) = sin x, f(x) = cscx (d) f(x) = tan x, f(x) = cosx Mark Value: 2 7. Match the following characteristics for each reciprocal trigonometric graph. Some may be used more than once. {(x) = csc x f(x) = secx f(x) = cotx (a) X-intercepts are at = + nn, ne I (b) Range is {yER/y S -1, y 21} (c) Period is it (d) Y-intercept of (0,1) (e) Contains vertical asymptotes Mark Value: 4 Communication: 8. Describe any transformations that may be applied to f(x) = tan 8 in order to transform it into the graph of its reciprocal, f (x) = cote. Mark Value: 3 9. To test the resistance of a new product to temperature changes, a product is placed in a temperature-controlled environment. The temperature in this environment can be described by a sine function. The maximum temperature is 120 degrees, the minimum temperature is -60 degrees, and the temperature at t = 0 is 30 degrees. After t = 0, the temperature begins by increasing to the maximum, and it takes 12 hours to complete one cycle. State the amplitude, period, and phase shift of the sine function. Graph the data and determine the equation of the sine function that models the data. Mark Value: 5 Application: 10. Determine the exact value of each of the following: (e) sin + sec (f) tan (8) cos S (h) esc(-#) + cot Mark Value: 4 11. If csco = -12 and 0 is in the third quadrant, determine all possible values of the expression tan 0 + 3 sece. State all possible values of 0 in radians. Mark Value: 8