Graphs of trigonometric functions

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Graphs of trigonometric functions

  1. 1. TARUNGEHLOT Graphs of Trigonometric FunctionsSine CosinePeriod = 2  Period = 2  y = a sin (bx + c) y = a cos (bx + c)amplitude = a amplitude = a 2 2period = period = b b c cphase shift = phase shift = b bone cycle can be found by solving: one cycle can be found by solving: 0  bx  c  2 0  bx  c  2Tangent CotangentPeriod =  Period = x –intercepts at  n  x –intercepts at  n  2vertical asymptotes at x =  n 2 vertical asymptotes at x =  n y = a tan (bx + c) y = a cot (bx + c)
  2. 2.  period = period = b b c cphase shift = phase shift = b bsuccessive vert. asymptotes for one branch: successive vert. asymptotes for one branch:   2  bx  c   2 0  bx  c  Cosecant SecantPeriod = 2  Period = 2 Vertical asymptotes at x =  n  Vertical asymptotes at x =  n 2 y = a csc (bx + c) y = a sec (bx + c) 2 2period = period = b b c cphase shift = phase shift = b bone cycle can be found by solving: one cycle can be found by solving: 0  bx  c  2  3  bx  c  2 2To graph y = a csc (bx + c):First graph y = a sin (bx + c); draw the To graph y = a sec (bx + c):vertical asymptotes at the x-intercepts; vertical asymptotes at the x-ints, First graph y = a cos (bx + c); draw thetake the reciprocals. vertical asymptotes at the x-intercepts; vertical as take the reciprocals.Summary: period x-intercepts y-intercepts Vertical asymptotes y = sin x 2 n 0 none y = cos x 2  1 none  n 2 y = tan x  n 0  x   n 2
  3. 3. y = cot x   none x  n  n 2y = sec x 2 none 1  x   n 2y = csc x 2 none none x  n

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