Precalculus

• degrees → radians

  $𝝅/180$
• radians → degrees

  180/π
• is cosine x or y?

  x
• is sine x or y?

  y
• what is the arc length formula?

  s = r ⋅ θ

  s is the arc length,

  r is the radius of the circle,

  θ is the central angle in radians.
• angular speed is

  linear speed/radius
• linear speed = s/t

  s is arc length, t is time
• angular speed = θ/t

  θ is angle of rotation, t is time
• what is a good method when doing linear & angular speed word problems?

  set up proportion and cross cancel units
• the radius of a unit circle is 1
• cot= x/y (in terms of x &y)
• tan= y/x (in terms of x &y)
• csc= 1/y (in terms of x &y)
• sec= 1/x (in terms of x &y)
• csc= 1/sin (in terms of sin & cos)
• sec = 1/cos (in terms of sin & cos)
• tan = sin/cos ( in terms of sin & cos)
• cot = cos/sin (in terms of sin & cos)
• what is the pythagorean identity? (sin & cos)

  $cos^2x +$$sin^2x =$$1$
• what is the pythagorean identity? (cot & csc)

  $cot^2x +$$1 =$$csc^2x$
• what is the pythagorean identity? (tan & sec)

  $tan^2x +$$1 =$$sec^2x$
• cofunction identity: sine

  $sin(π/2 -x) =$$cos x$
• cofunction identity: cosine

  $cos(π/2 -x)=$$sinx$
• cofunction identity: tangent

  $tan(π/2-x)=$$cotx$
• even/odd identity: sine

  $sin(-x) =$$-sinx$
• even/odd identity: cosine

  $cos(-x)=$$cos x$
• even/odd identity: tangent

  $tan(-x)=$$-tanx$
• which function is the exception with even/odd identities?

  cosine (there is no negative)
• angle of elevation goes up from the horizontal
• angle of depression goes down from the horizontal
• equation of cosine graph is

  $y=$$a⋅cos[b(x-h)]+$$k$
• equation of sine graph is

  $y=$$a⋅sin[b(x-h)]+$$k$
• in trig graphs, a represents the amplitude which is half the distance from the max to the min. it is the distance from the max/min to the midline.
• in trig graphs, b changes the period of the graph. it is a horizontal st/sh.
• horizontal st/sh of trig graphs:

  $1/|b|$
• period of trig graphs:

  $|2π/b|$
• in trig graphs, h represents a phase shift or horizontal translation
• in trig graphs, k represents a vertical translation
• circle formula: 


  $(x-h)^2 +$$(y-k)^2 =$$r^2$
• parabola formula (horizontal):


  $(y-k)^2=$$4p(x-h)$