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Graphing Trig Functions

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  • Which functions begins and ends with a max/min, and has a max/min halfway through its period?
    y=cos(x)
  • For the function y=atan(bx) + d, which value of b will give the function a period of 3?
    π/3
  • Which function has a zero whenever y=sin(x) = 0?
    y=tan(x)
  • Which functions have vertical asymptotes whenever cos(x)=0? (you have to say both)
    y=sec(x) and y=tan(x)
  • What graph is this?
    y = 2sin(2x)
    y = -2cos(2x)
    y = -2sin(2x)
    y = 2cos(2x)
  • If you graphed the function y=sin(2x), at what positive value of x would the function reach a maximum first?
    π/4
  • If you graphed the function y=cos(1/2x), at what positive value of x would the function reach a minimum first?
  • What graph is this?
    y=tan(x)
    y= - cot(x)
    y=cot(x)
    y = - tan(x)
  • What graph is this?
    y=tan(x)
    y=cot(x)
    y = - tan(x)
    y= - cot(x)
  • From [0, 2π] {included} where does y=cot(x) have vertical asymptotes? (Name all of them)
    0, π, 2π
  • Determine the period y = 5tan(2x)
    π/2
  • What graph is this?
    y=3sin(x)
    y=3cos(x)
    y= -3sin(x)
    y= -3cos(x)
  • Which function has a zero whenever cos(x) = 0?
    y = cot(x)
  • What graph is this?
    y=csc(x)
    y=csc(2x)
    y=-sec(x)
    y=sec(1/2x)
  • Determine the period: y= -csc(5x) -11
    2π/5
  • What graph is this?
    y=tan(x)
    y=cot(x)
    y=-cot(x)
    y=-tan(x)
  • What graph is this?
    y=-csc(x)
    y=-sec(x)
    y=sec(1/2x)
    y=csc(x)
  • Determine the period: y = -3cot(1/3x)
  • Determine the period: y=7cos(1/4x)
  • What graph is this?
    y = - cot(x)
    y= - tan(x)
    y=cot(x)
    y=tan(x)
  • What graph is this?
    y= 2cos(2x)
    y= -2cos(2x)
    y= 2sin(2x)
    y= -2sin(2x)
  • What graph is this?
    y = - tan(x)
    y= - cot(x)
    y=tan(x)
    y=cot(x)
  • For the function y=acos(bx) + d, which value of b will give the function a period of 18?
    π/9
  • For the function y=acot(bx) + d, which value of b will give the function a period of 1/2?
  • Which functions have vertical asymptotes wherever sin(x)=0 (you have to say both)
    y=csc(x) and y=cot(x)
  • What graph is this?
    y=cos(2x)
    y=cos(1/2x)
    y=cos(x)
    y=2cos(x)
  • Determine the period: y=sin(3x)
    2π/3
  • From [0,2π] {included} where does y=tan(x) have vertical asymptotes? (Name all of them)
    π/2, 3π/2
  • What graph is this?
    y=sin(2x)
    y=2sin(x)
    y=sin(x)
    y=sin(1/2x)
  • For the function y=asin(bx) + d, which value of b will give the function a period of 7?
    2π/7
  • Which function begins and ends at the midline, and passes through the midline halfway through its period?
    y=sin(x)