Wave Function

Question 1

Write 4cosx+3sinx in kcos(x-a)

Answer 1

Expand the brackets using compound formula, bring a to front, compare with original (sina=3 etc) and use trig identities to get tana=4/3. Look at double tricked quadrant to find a. Square both sides to find k using a trig identity and re-write as required.

Question 2

Maximum and Minimum Values

Answer 2

Rewrite as appropriate. Use amplitude for y max and min value. For max and min x value, occurs when cos(x-1.33) occurs when equal to 1 then -1. This is like co-ordinates.

Question 3

Solving Equations

Answer 3

Rewrite as cos(x-a) for example. Solve algebraically for x values.

Question 4

Sketch graphs y=pcosx+qsinx

Answer 4

Rewrite in desired form. Use amplitude for max and min values, use graph movements, find y intercept when x=0. Annotate fully.