Combining two trig terms into one?

  • Thread starter DWill
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If I have 2 cosine terms added together, how would I combine them into one cosine term?

Ex:
A) 3 cos(2t)
B) cos(2t - pi/2)

Thanks

PS. I don't think the sum to product formulas work, I'm wondering how to combine them into a single cosine term?
 
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These kind of operations are easiest with complex numbers.
[tex]3\cos(2t)+\cos(2t-\frac{\pi}{2})=\Re\left(3\exp(2ti)+\exp(2ti-\pi i/2)\right)=\Re\left(\exp(2ti)(3-i)\right)[/tex]
[tex]=\Re\left(\exp(2ti)\sqrt{10}\exp(-i\arctan\frac{1}{3})\right)=\sqrt{10}}\cos(2t-\arctan(\frac{1}{3}))[/tex]
 

Mentallic

Homework Helper
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You can solve this by the use of the auxillary angle technique.

[itex]cos\left((2t)-\pi/2\right)=sin(2t)[/itex] (you can confirm this by expanding the LHS, but this is a trigo identity you may remember having learnt).

Now let [itex]3cos(2t)+sin(2t)\equiv Rsin(2t-\theta)[/itex]

expand the RHS and then equate like terms. Solve the system of 2 equations in R and [itex]\theta[/itex] and then you'll have the original equation in terms of just one trigonometrical expression.
 

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