Trigonometry

• Midpoint Formula

  $( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )$
• Distance Formula

  $d(A,B)=$ \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
• Equation of a circle

  $(x-h)^2+$$(y-k)^2=$$r^2$
• standard form of a circle

  $x^2+$$y^2=$$r^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)+$$c$
• shifts downward

  $f(x)-c$
• Shifts to the right

  $f(x-c)$
• shifts to the left

  $f(x+c)$
• Flips from up to down

  $y=$$-f(x)$
• flips from right to left

  $y=$$f(-x)$
• $y=$$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 =$$\frac{\pi}{2} , \pi, \frac{3\pi}{2}, 2\pi$
• $cos(x)=$$x$
• $sin(x) =$$y$
• $tan(x)=$$\frac{y}{x}$
• $csc(x) =$$\frac{1}{sin(x)}$
• $sec(x) =$$\frac{1}{cos(x)}$
• $cot(x) =$$\frac{1}{tan(x)}$
• $tan(x) =$$\frac{sin(x)}{cos(x)}$
• $cot(x) =$$\frac{cos(x)}{sin(x)}$
• $sin^2x+$$cos^2=$$1$

  pythagorean identity
• $tan^2x+$$1=$$sec^2x$
• $cot^2x+$$1=$$csc^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=$$a \:sin \:kx$
• a = amplitude ,(vertical stretch or shrink)

  k = period, (changes length of wavelength)

  $y=$$a\:cos\: kx$
• How to find period of y= a sin kx and y= a cos kx?


  $\frac{2\pi}{k}$