Wave function

Question 1

How to express acosx + bsinx in the form kcos(x+-a) or ksin(x+-a)

Answer 1

Write whatever form is asked in underneath equation given.
Using trig identities expand the brackets of eq asked for
Equate coefficients
Solve for k(square and add = k^2 then square root k^2)
Solve to find a and using ksinx/kcosx
Find which quarter it is in by one with two ticks solve for a.
Rewrite equations with original equations then underneath expressed with equation asked for.

Question 2

Given choice which version of wave function should be used

Answer 2

If starts with cos use cos wave function and vice versa

Question 3

How to find maximum and minimum values of a wave function

Answer 3

Use wave graph

Question 4

acosx + bsinx =c

Answer 4

Put left hand side into wave function then solve as usual

Question 5

What if question has 2x or 3x

Answer 5

Put into wave function as usual then take 2x or 3x into account when solving