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7.5 Graphs of All Trig Functions y = sin (x) domain: all real numbers; range: –1 ≤ y ≤ 1; fundamental period = 360° or 2π y = cos (x) domain: all real numbers; range: –1 ≤ y ≤ 1; fundamental period = 360° or 2π y = tan (x) domain: all real numbers except 90° + 180° n or π/2 + πn range: all real numbers # # fundamental period: 180° or π radians ! 4 y = cot (x) domain: all real numbers except 0° + 180° n or 0 + πn range: all real numbers# # fundamental period: 180° or π radians ! 4 y = csc (x) domain: all real numbers except 0° + 180n or 0 + πn range: y ≤ –1 or y ≥ 1# # fundamental period: 360° or 2π y = sec (x) domain: all real numbers except 90° + 180n or π/2 + πn range: y ≤ –1 or y ≥ 1# # fundamental period: 360° or 2π Comparing sin(x), cos(x) and tan(x): Comparing sin(x) and csc(x) Comparing cos(x) and sec(x) 9/25/15# # # # # # # # # # # AM1 7.5 B GRAPHING THE SIX FUNDAMENTAL TRIG FUNCTIONS 1) Graph y = sin(x) and y = csc(x) For y = sin(x) domain: _________ range________ fundamental period _________ For y = csc(x) domain: _________ range________ fundamental period _________ 2) Graph y = cos(x) and y = sec(x) For y = cos(x) domain: _________ range________ fundamental period _________ For y = sin(x) domain: _________ range________ fundamental period _________ 3) Graph y = tan(x) domain: _________ range________ fundamental period _________ 4) Graph y = cot(x) domain: _________ range________ fundamental period _________ 9/25/13# # # # # # # # # AM1# # 7.5B Homework from the book: (p. 285 #5, 9, 10, 11, 12, 17, 21) 5) Express each of the following in terms of a reference angle # a) tan(820º) = _______# # b) sec(290º) = ________ # c) cot(185º) = ________# # d) csc(4) = _________ 9) Sketch a graph of cot ! versus ! for – π ≤ ! ≤ 3π. Be sure to show where any vertical asymptotes occur. 10) On a single set of axes, graph y = sin (x) and y = csc (x), showing at least two full periods of each function. Using the reciprocal relationship between sine and cosecant, explain the features (x-intercepts, vertical asymptotes, periodicity, and so on) of the cosecant graph. 11) On a single set of axes, sketch the graphs of y = tan (x) and y = 2x. How many solutions does the equation tan (x) = 2x have? 12) On a single set of axes, sketch the graphs of y = sin (x) and y = sec (x). How many solutions does the equation sin (x) = sec (x) have? 17) Find the values of the other 5 trigonometric functions is tan(x) = # 3 and π < x < 2π . 4 cos(x) = ___# sin(x) = ___# cot(x) = ___# sec(x) = ___# csc(x) = ___ ⎛π⎞ ⎛π⎞ ⎛π⎞ ⎛π⎞ ⎛π⎞ 21) Show that 1+ tan 2 ⎜ ⎟ = sec 2 ⎜ ⎟ . Note: tan 2 ⎜ ⎟ means tan ⎜ ⎟ ⋅ tan ⎜ ⎟ ⎝ 3⎠ ⎝ 3⎠ ⎝ 3⎠ ⎝ 3⎠ ⎝ 3⎠ #