Warm Up Jan. 24th • Graph the following:

1. f(x) = -2 + sin3x

2. g(x) = 2cos(x – ) + 12

3

Sum & Difference of Sine & Cosine Graphs

Use knowledge of sine and cosine as well as properties of their graphs, to apply to

the sum or difference of the functions.

Use your graphing calculator to sketch the graph of y = 3sin(2x – 1) + 4cos(2x + 3)

• What is the period of the graph?• What is the amplitude of the graph?• Rewrite y in the form asin(b(x + c)).

From the previous example: what do the sine and cosine terms have in common?y = 3sin(2x – 1) + 4cos(2x + 3)

If the periods of the sine and cosine terms are different, then the combination will not be a sine (or cosine) curve, but will still be periodic.

Let f(x) = sin(2x) + 4cos(3x)• Determine the period of f.• Determine the range of f.

Sketch without using a graphing calculatory = cos(2x) + sin(4x)

x

Cos(2x)

Sin(4x)

Cos(2x)+

Sin(4x)

You Try! 1) Let f(x) = sin( ½ x) - 2cos(½ x - 1). Rewrite f(x) in

the form asin(b(x + c)).

2) Let g(x) = sin(3x) + 5cos(4x). a) Determine the period of f.

b) Determine the range of f.

3) Sketch without a graphing calculator.

f(x) = cos(8x) – sin(2x)

Midterms…• You need to understand and fix your mistakes.• On separate paper, number and neatly write the

questions you missed.• For each question, write the correct answer (full

answer, not B) and why you got it wrong.– Did you drop a negative, miscalculate or use the wrong

formula.• Due back Feb 1st (A day), Feb 2nd (B day)