Trigonometry

    Cards (34)

    • Midpoint Formula
      (x1+x22,y1+y22)( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )
    • Distance Formula
      d(A,B)=d(A,B)= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    • Equation of a circle
      (xh)2+(x-h)^2+(yk)2=(y-k)^2=r2r^2
    • standard form of a circle
      x2+x^2+y2=y^2=r2r^2
    • Domain
      all possible x-values
    • Range
      all possible y-values
    • what does [0,25] U [35,40] mean?
      that [] is a specific interval, stops, then continues []
    • Shifts upwards
      f(x)+f(x)+cc
    • shifts downward
      f(x)cf(x)-c
    • Shifts to the right
      f(xc)f(x-c)
    • shifts to the left
      f(x+c)f(x+c)
    • Flips from up to down
      y=y=f(x)-f(x)
    • flips from right to left
      y=y=f(x)f(-x)
    • y=y=cf(x)cf(x)
      if c>1, it will stretch vertically by a factor of c
      if 0<c<1, it will shrink vertically by a factor of c
    • f is even if f(-x) = f(x) for all x in the domain of f
      f is odd if f(-x)= -f(x) for all x in the domain of f
    • Terminal point are determined by
      t=t =π2,π,3π2,2π \frac{\pi}{2} , \pi, \frac{3\pi}{2}, 2\pi
    • cos(x)=cos(x)=x x
    • sin(x)=sin(x) =y y
    • tan(x)=tan(x)=yx \frac{y}{x}
    • csc(x)=csc(x) =1sin(x) \frac{1}{sin(x)}
    • sec(x)=sec(x) =1cos(x) \frac{1}{cos(x)}
    • cot(x)=cot(x) =1tan(x) \frac{1}{tan(x)}
    • tan(x)=tan(x) =sin(x)cos(x) \frac{sin(x)}{cos(x)}
    • cot(x)=cot(x) =cos(x)sin(x) \frac{cos(x)}{sin(x)}
    • sin2x+sin^2x+cos2=cos^2=11
      pythagorean identity
    • tan2x+tan^2x+1=1=sec2x sec^2x
    • cot2x+cot^2x+1=1=csc2xcsc^2x
      pythagorean identity
    • Graph of sin(x)
    • Graph of sin(X)
      • Domain: (-∞, ∞)
      • range [-1,1]
      • period is 2π
      • goes through the origin
      • odd function
    • Graph of cos(x)
    • Graph of cos(x)
      • Domain (-∞,∞)
      • range [-1,1]
      • period is 2π
      • even function
    • a = amplitude ,(vertical stretch or shrink)
      k = period, (changes length of wavelength)
      y=y=asinkxa \:sin \:kx
    • a = amplitude ,(vertical stretch or shrink)
      k = period, (changes length of wavelength)
      y=y=acoskxa\:cos\: kx
    • How to find period of y= a sin kx and y= a cos kx?

      2πk\frac{2\pi}{k}