# a(x) = 5 sin x b(x) = 4 cos (2x + pi/3) 1.) Give the equation for the combined equations 2.) Sketch the graph of the combined equations

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`a(x)=5sinx` , `b(x)=4cos(2x+pi/3)`

`a(x)+b(x)=5sinx+4cos(2x+pi/3)`

Using `cosalpha=sin(pi/2-alpha)` we can rewrite as :

`a(x)+b(x)=5sinx+4sin(pi/2-(2x+pi/3))`

`=5sinx+4sin(pi/6-2x)`

The graph:

If you want to combine the equations, you may add or subtract them such that:

a(x) + b(x) = 5 sin x + 4 cos (2x + pi/3)

or

a(x) - b(x) = 5 sin x - 4 cos (2x + pi/3)

or

b(x) - a(x) = 4 cos (2x + pi/3) - 5 sin x

You need to sketch the graphs of the combined equations such that:

a(x) + b(x) = 5 sin x + 4 cos (2x + pi/3)

a(x) - b(x) = 5 sin x - 4 cos (2x + pi/3)

b(x) - a(x) = 4 cos (2x + pi/3) - 5 sin x