# Graphing trig functions without calculus

1. Oct 25, 2009

### nietzsche

1. The problem statement, all variables and given/known data

I'm in a first-year analysis course, and this question was given by my prof. as practice for her midterm test.

"Sketch the graph of the function

$$\begin{equation*} f(x) = \text{sin} 2x + \sqrt{3} \text{cos} 2x \end{equation*}$$

Determine the amplitude, the frequency and the phase of $$f(x)$$.

2. Relevant equations

3. The attempt at a solution

It's been a really long time since I've done graphing transformations of trig functions without calculus, so I truthfully don't remember how to do this.

I can see they both have period pi, and sin(2x) has amplitude 1 and sqrt3 cos(2x) has amplitude of sqrt3.

I don't know how to determine the highest point on the graph (amplitude), and I don't know how to determine the phase.

Last edited: Oct 25, 2009
2. Oct 25, 2009

### Dick

3. Oct 25, 2009

### nietzsche

4. Oct 25, 2009

### nietzsche

Last edited: Oct 25, 2009
5. Oct 25, 2009