Graphing Trig Functions

  • midline↔horizontal center line about which the sinusoidal function oscillates above and below
  • amplitude↔height from the center line to the peak of a periodic function
  • period↔wavelength of a sine or cosine graph
  • MAP it!↓
    • Midline
    • Amplitude
    • Period
  • General Form of a Trig Function↔y = h + A(sin|cos|tan|csc|sec|cot) k\theta + c (k affects frequency, h affects midline)
  • horizontal shift↔\frac{-c}{k}
  • Period of sin & cos↔\frac{2\pi}{k}
  • Graphs of csc & sec↓
    • asymptotes @ zeros
    • peaks⇔valleys
    • are parabolic
  • Graph of tan
    • I'm a zero, and I spread out my arms 1/2-period long.
    • is like x^{3}
  • Graph of cot↓
    • I'm an asymptote, and I spread out my arms 1-period long.
    • is ike -x^{3}
  • Period of tan & cot↔\frac{\pi}{k}
  • arcsin domain→[−1, +1]
  • arcsin range→Q IV, I: [−π/2, +π/2]
  • arccos domain→[−1, +1]
  • arccos range→Q I, II: [0, π]
  • arctan domain→all reals
  • arctan range→Q IV, I: (−π/2, +π/2)