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Chapter 7 Review Complete the chart then graph each function on the provided graphs. If it does not apply or there is not one, state so. [1 pt each box, total 24 pts] Function Amplitude Period Phase Shift Vertical Shift 1 x 1 2 y 3cos 2x 4 y 2 tan 1 y sin 2 x 3 2 y csc x 2 y sec 2 x 2 y 2cot x 3 Graph each of the above functions. Make sure you graph ONE complete cycle to the left and to the right after you shifted the origin. [5 pts each, total 30 pts] 1) y 2 tan 1 x 1 2 4) y csc x 2 2) y 3cos 2x 4 5) y sec 2 x 2 1 3) y sin 2 x 3 2 6) y 2cot x 3 Multiple Choice: Write the answer for the following problems on the line provided. [4 pts each, total 24 pts] _____ 7) The period for y 4sin ( x 1) 1 is: A) 1 B) C) 4 D) 2 _____ 8) Which trigonometric function listed is EVEN? A) sine B) cosecant C) tangent D) cosine E) None of these E) None of these _____ 9) What is the domain for y 9cos 2 x 1 A) , B) 1,1 C) 8,10 _____10) Where are the asymptotes for y tan x ? A) k where k is any integer. B) k where k is any ODD integer. k C) where k is any integer. 2 k D) where k is any ODD integer. 2 E) None of these. _____11) Where are the asymptotes for y csc x A) k where k is any integer. B) k where k is any ODD integer. k C) where k is any integer. 2 k D) where k is any ODD integer. 2 E) None of these. _____12) Given the graph to the right, determine which equation it best resembles. A) y = 4 sin 2x + 1 B) y = 3 sin 4x C) y = 3 sin 2x + 1 D) y = 3 sin 2x – 1 E) y = 2 sin 4x + 1 D) 2 , 2 E) None of these Modified True/False. Determine if the state is true or false. IF it is false, correct the underlined word. [2 pts each for T/F and 2 pts to correct the false]. True False _______________ 13) Period is defined by the number of times you see a complete cycle from 0 to 2. True False _______________ 14) Sine and Cosecant are the only 2 trigonometric functions that when graphed do not have asymptotes. True False _______________ 15) Tangent does not have an amplitude since it has a range of , . Write the equation the periodic function with the following changes [4 pts each]: 16) y = sin x with an Amplitude of ¼ , period of , phase shift of right and vertical 4 shift of up 2 . 17) y = tan x with a reflection across the x-axis, period of 4, phase shift of 2 , and 3 vertical shift of down 1. 18) Explain how knowing the unit circle helps you graph y = sin x and y = cos x. You must explain this in AT LEAST 3 sentences. _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ _______________________________________________________________________ 19. Find all solutions from 0 to 2. (hint: You may want to use the unit circle to help you find all of them.) 1 sin 1 . 2