1. Graphs of Cosine Functions (part 2)
I. Graphing the cosine function f(x) = cos θ.
A) Use the unit circle to find cos θ (width values).
1) cosine is the width, x, when θ is the angle.
2) θ = θ = π/ θ = π θ = 3π/2 θ = 2π
0° ° ° ° °
(1, 0) (0 , 1) (-1, 0) (0 , -1) (1, 0)
x = x = x = x = x = 1
3) To graph, we plot these 5 points (min / max / x-int)
and connect them with a curved line. 1 2π
π/2
3π/2 π -1

2. Graphs of Cosine Functions (part 2)
I. Graphing the cosine function f(x) = cos θ.
B) The cos graph repeats after every 2π (one cycle)
1) The graph from 0 to 2π is called the Period.
C) The height of the graph is called the Amplitude.
1) This is the range (the y values of the graph).
D) Sideways shifts are Horizontal Translations. 1) These horizontal shifts are phase shifts
E) Standard form of a sine function.
1) f(x) = A cos (B(x + C)) + D
a) Notice we have to factor out the B term.

3. Graphs of Cosine Functions (part 2)
II. Transformations of the Cosine Function.
A) We need to get it into standard form.
1) f(x) = A cos (B(x + C)) + D or y = D + A cos (B(x + C))
B) Amplitude (the A term). This is the height. Amp = | A |.
1) Go the A value above and below the origin.
C) Period (the B term). Remember to factor out the B value.
1) The period = 2π/B.
a) Big B values are horiz shrinks, small B’s stretch it.
D) Phase Shift (the C term). This moves the graph sideways.
1) Set the (x + C) part = 0 to find the shift (changes sign).
E) Vertical Shift (the D term). Moves the graph up or down.
1) Moves all the min / max / x-int points up or down by D.

4. Graphs of Cosine Functions (part 2)
III. Graphs of the cos function y = D + A cos (B(x + C)).

5. Graphs of Cosine Functions (part 2)
III. Graphs of the cos function y = D + A cos (B(x + C)).