#1**+1 **

\(2\cos^2{x} = \cos{x}\)

We can divide both sides by cosx

This gives us:

\(2\cos{x} = 1\)

Dividing by 2 on both sides, we get:

\(\cos{x} = \frac12\)

The values for which this is true in the interval \([0,2\pi)\) are

\(\cos{\pi\over3}\) radians (cos 60 degrees) and also

\(\cos{5\pi\over6}\)radians(cos 300 degrees)

jfan17 Apr 17, 2020

#2**+1 **

that makes sense for those 2! thank you. would we need to include 0 and pi as well as options?

jjennylove
Apr 17, 2020

#4**+2 **

No, we in fact don't include 0 or pi. What's your reasoning for that?(Just curious).

The cosine of 0 is equal to 1. However,

2* 1^2 is not equal to 1, meaning that 0 does not follow through with our given equation.

Let's check \(\pi\)

the cosine of \(\pi\) = -1. Similarly,

2 * (-1) ^2 is not equal to -1, meaning that pi does not follow through with our given equation either.

jfan17
Apr 17, 2020

#6**0 **

hmm okay, yes i was confused. based upon your explaination you are correct we would not need to include them. thank you!

jjennylove
Apr 17, 2020

#3**+2 **

[ ] These brackets means "Include".

() These parantheses means "Do not include".

However, this doesn't come in this case. Look at jfan's answer above.

CalTheGreat Apr 17, 2020