Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions Mrs. Grieser Name: _______________________________________ Date: ________________ Block: __________ Graphing Trig Functions TEST STUDY GUIDE Test covers: Know domain, range, period, and intercepts of the six parent trig functions. Find amplitude, period, phase shift, and vertical displacement, as applicable, for all six trig functions. Graph the functions applying transformations using this information. Writing equations of trig functions from a verbal description of amplitude, period, phase shift, and/or vertical displacement, or from a given graph. Practice Questions: 1) Graph each function, finding the requested information. a) y = sin x b) y = cos x Domain_________ x-ints _________ Domain_________ x-ints _________ Range _________ y- int _________ Range _________ y- int _________ Period _________ Period _________ c) y = tan x d) y = cot x Domain_________ x-ints _________ Domain_________ x-ints _________ Range _________ y- int _________ Range _________ y- int _________ Period _________ Period _________ Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions e) y = csc x f) Mrs. Grieser Page 2 y = sec x Domain_________ x-ints _________ Domain_________ x-ints _________ Range _________ y- int _________ Range _________ y- int _________ Period _________ Period _________ 2) For each trig function below, identify the applicable values: amplitude, period, phase shift, vertical displacement, and whether graph is reflected. a) y = sin 6x b) y = - 5cos x c) y = - sin 2 x 2 3 d) y = 3cos3x 2 e) y = - 2sin x 5 6 f) y = csc g) y = cos 2 3 x x h) y = 1 4sec 10 x i) y = - 1 3cot2 x - 6 j) y = 2 5tan 8 x 3 Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions Mrs. Grieser Page 3 3) Graph the trig functions, finding the applicable values first: amplitude, period, phase shift, vertical displacement, and whether graph is reflected. a) x y 4 cos 3 amplitude: _______ b) y 4 sin 2 x amplitude: _______ period: ______ period: ______ c) x y csc 3 amplitude: _______ d) y cot 2 x amplitude: _______ period: _______ period: ______ e) y sin x 4 amplitude: _______ period: _______ f) y tan x 2 amplitude: _______ period: _______ Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions g) y 2 sin3x 2 amplitude: _______ period: ______ h) y Mrs. Grieser Page 4 1 cos x 2 2 4 amplitude: _______ period: ______ 4) Given the graph, find the amplitude and period, then write a trig function. a) b) 5) Write an equation of a cosine function with amplitude 3, a period of π, a phase shift of to the left, and translated 1 unit up. 6) Write an equation of a sine graph with a phase shift right 3, a period of 5π, a vertical translation down 6, and an amplitude of 3. 4 Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions Mrs. Grieser Page 5 STUDY GUIDE ANSWERS 1) a) D=(-∞, +∞); R=[-1, 1]; period: 2π; xints: nπ ; y-int: 0 b) D=(-∞, +∞); R=[-1, 1]; period: 2π; x-ints: c) D=all R except d) D=all R except n ; R=(-∞, +∞); period: π; x- 2 n ; y-int: 1 2 n ; R=(-∞, +∞); ints: 2 n ; y- period: π; x-ints: n ; y-int: 0 int: none e) D=all R except n ; R=(-∞, -1]U[1, ∞); period: 2π; x-ints:none; yint: none f) D=all R except 2) a) amp.:1; period: 2 1]U[1, ∞); period: 2π; x-ints:none; y-int: 1 3 c) amp:1; period π; phase shift: up 2; reflected e)amp: 2; period: 2π; phase shift: down 5; reflected g) amp: 1; period: 6 n ; R=(-∞, - b) amp.:5; period: 2; reflected left; translate 3 right; translate 6 d)amp: 3; period: 2 ; phase shift: left; 3 3 translate down 2 f) amp: n/a; period: 4 i) amp: n/a; period: ; phase shift: right; 2 6 h) amp: n/a; period 40; translate up 1 j) amp: n/a; period 8; phase shift: 3 right; translate up 2 translate down 1 3) a) b) Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions Mrs. Grieser Page 6 c) d) e) f) g) h) 4) a) amp: 4; period: 2π; y=4cos x b) amp:5; period 2π; y = -5cos x 5) y = 3cos2 x 6) y sin 2 x 3 6 5 1 or y = 3cos 2x 1 4 2