Topic 3: Trigonometric Functions

Graphing sine and cosine functions

y \= asin(b(x-c)) + d OR y \= acos(b(x-c)) + d

General equation of a trigonometric function

amplitude

the absolute value of a

(max-min)/2

how to find the amplitude

period

the horizontal distance between two maximum or two minimums OR two times the horizontal distance between a maximum and a minimum

period \= (2π)/b

how to find the period

find any point on the principal axis where the curve goes up after

how to find the phase shift, c, for a sine graph

find any maximum point

how to find the phase shift, c, for a cosine graph

a

affects vertical stretch

b \> 0

affects horizontal stretch

c

affects horizontal translation

d

affects vertical translation

y \= d

principal axis

(max + min)/2

how to find the principal axis

(0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0)

5 major points of a sine parent graph

(0, 1), (π/2, 0), (π, -1), (3π/2, 0), (2π, 1)

5 major points of a cosine graph

the number of periods

Iterations in SinReg 1

how long does it take to complete one cycle (time)

Period in SinReg 1

What does a sine graph look like?

the sine graph begins at the principal axis

What does a cosine graph look like?

the cosine graph begins at a maximum

Equation of a tangent function

y = atan(b(x - c)) + d

a = vertical dilation

period = π/b

c > 0 shifts the graph to the right

c < 0 shifts the graph to the left

y = d: principal axis