1. ## cosine equation

Right, im confused by this question...

Find all the roots in the range -2π < x < 2π of the equation cos(2x) = 0.5 giving all the answers in radians as multiples of π.

At first i thought it would be a (varying) cosine wave but how does that make sense, where is the 'y'? I thought by 'find the roots' it meant finding the angles at which the wave goes through the x axis between that range...

any help. please? this is the last question and its in for tomorra

2. Originally Posted by jugglingpirate
Right, im confused by this question...

Find all the roots in the range -2π < x < 2π of the equation cos(2x) = 0.5 giving all the answers in radians as multiples of π.

At first i thought it would be a (varying) cosine wave but how does that make sense, where is the 'y'? I thought by 'find the roots' it meant finding the angles at which the wave goes through the x axis between that range...

any help. please? this is the last question and its in for tomorra
$
\cos(y)=0.5 \Rightarrow y=\pm\pi/3+2n\pi,\ n=0,\pm1,\pm2,...
$

so if $2x=y$, the roots are: $x=\pm\pi/6+n\pi,\ n=0,\pm 1,\pm 2,...$.

Now find the values of $n$ which leave $x$ in the required range.

CB