Circular functions

Radians and degrees

Exact values

and graphs

where
is the -dilation (amplitude)
is the -dilation (period)
is the -shift (phase)
is the -shift (equilibrium position)

Domain is
Range is ;

Graph of starts at . Graph of starts at .

Mean / equilibrium: line that the graph oscillates around ()

Solving trig equations

  1. Solve domain for
  2. Find solutions for
  3. Divide solutions by




Amplitude

Amplitude of means graph oscillates between and in -axis

produces straight line
inverts the phase ( becomes , vice vera)

Period

Period is
produces straight line
inverts the phase

Phase

moves the graph left-right in the axis.
If , the graph has no actual phase shift.

Symmetry

Pythagorean identity

Complementary relationships

graph

where
is -dilation (period)
is -dilation ( amplitude)
period is
range is
roots at
asymptotes at
Asymptotes should always have equations and arrow pointing up