# Finding trig identity on calculator?

• Jun 12th 2013, 06:29 PM
FatimaA
Finding trig identity on calculator?
EDIT: I actually went back and re watched the video a few times and realized that he disengaged the bottom two functions. I'm sorry if this took up anyone's time. Can anyone tell me how to graph functions simultaneously on a graphing calculator?

Hi. I'm following along on a precalculus video from my professor. In the very first problem, he graphs a trigonometric equation in the calculator to see if it is an identity. I'm not getting the same graph as he is, and I'm not sure what's wrong. I have it on zoom trig but my graph is different than his.

This is the problem:

Is cos2x = 2(cosx^2)-1 an identity?

Here is the video. It's the very first problem he covers.

142 Section 7.5 Solving Trigonometric Equations - YouTube

\displaystyle \begin{align*} \cos{(2x)} = 2\cos^2{(x)} - 1 \end{align*} is an identity.
Here's a nice proof of the angle sum identity for cosine: \displaystyle \begin{align*} \cos{ \left(\alpha + \beta \right) } = \cos{(\alpha )}\cos{(\beta )} - \sin{(\alpha )}\sin{(\beta)} \end{align*}
And in the case where \displaystyle \begin{align*} \alpha = \beta = x \end{align*} then that gives
\displaystyle \begin{align*} \cos{ \left( x + x \right) } &= \cos{(x)}\cos{(x)} - \sin{(x)}\sin{(x)} \\ \cos{(2x)} &= \cos^2{(x)} - \sin^2{(x)} \\ &= \cos^2{(x)} - \left[ 1 - \cos^2{(x)} \right] \textrm{ by the Pythagorean Identity} \\ &= \cos^2{(x)} - 1 + \cos^2{(x)} \\ &= 2\cos^2{(x)} - 1 \end{align*}