+0  
 
0
58
7
avatar+1898 

i am unsure how to solve this

 Apr 17, 2020
 #1
avatar+483 
+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)

 Apr 17, 2020
 #2
avatar+1898 
+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
avatar+483 
+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
avatar+1898 
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
avatar+1955 
+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.

 Apr 17, 2020
edited by CalTheGreat  Apr 17, 2020
 #7
avatar+1898 
+1

thank you!

jjennylove  Apr 17, 2020
 #5
avatar+109492 
+1

It is really good to see you all collaborating together :)

 Apr 17, 2020
edited by Melody  Apr 17, 2020

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