+499 \(2\cos^2{x} = \cos{x}\)
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)
+1995 that makes sense for those 2! thank you. would we need to include 0 and pi as well as options?
+499 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.
+1995 hmm okay, yes i was confused. based upon your explaination you are correct we would not need to include them. thank you!
+2095 [ ] These brackets means "Include".
() These parantheses means "Do not include".
However, this doesn't come in this case. Look at jfan's answer above.
