MHB Adding Trigonometric Functions

[TrigEatsMe]

I've muddled my way through the majority of my weekend assignment and I'm stuck on a problem where I need to add two formulas together.

1.) 20-10cos(x*pi/4)
2.) 30+20sin(x*pi/4)

I end up with a sinusoidal function which I can then graph and determine the max, min, etc.

We recently went over the addition/subtraction of trigonometric functions using formulas, but none of them match up with this kind of question. I'm missing something.

 

[Opalg]

I've muddled my way through the majority of my weekend assignment and I'm stuck on a problem where I need to add two formulas together.

1.) 20-10cos(x*pi/4)
2.) 30+20sin(x*pi/4)

I end up with a sinusoidal function which I can then graph and determine the max, min, etc.

We recently went over the addition/subtraction of trigonometric functions using formulas, but none of them match up with this kind of question. I'm missing something.

The formula you need here is the one that says $a\sin\theta - b\cos\theta = \sqrt{a^2+b^2}\sin(\theta - \phi)$, where $\tan\phi = \dfrac ba.$

 

[TrigEatsMe]

Got it -- weird how it clicks the following day sometimes. THanks! :)