ADDITION OF SINE AND COSINE: Consider the following:
g(x) =sin(x).
f(x) + cos(x)
and h(x) =f(x) +g(x)
The graph above shows the three functions.

It can be shown that the new function h(x) can be written at:
h(x) = V2sin (x +45)

1. Explain in words and show the steps on how the single trigonometric function for
h(x) could be found, using the original functions. for (9) marks

2.Write a full explanation or presentation on how the expression of
a sin(x) + b cos(x) can be written as a single trigonometric ratio. for (18) marks

3. Give the simplified expression for y = asin(x) + b cos (x) and comment on the new function's amplitude, period and shifts (vertical and horizontal) for (6) marks.

4.a. Application: Use your method above to describe how it can be used to find
the general solution for a sin(x) + b cos(x) = 0. for (4) marks

b. Give an example. for (4) marks
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