Thread: trig equation

Find all values of theta in the interval 0<theta<360

2 cos^2 theta - 1=0

Originally Posted by blame_canada100

Find all values of theta in the interval 0<theta<360

2 cos^2 theta - 1=0

$\displaystyle 2\cos ^2 \theta -1 = 0 $

$\displaystyle \cos ^2 \theta = \frac{1}{2}$

$\displaystyle \cos \theta = \mp \frac{1}{\sqrt{2}}$

theta equal the angle 45 in all quarters

Hello blame_canada100

Originally Posted by blame_canada100

Find all values of theta in the interval 0<theta<360

2 cos^2 theta - 1=0

Alternatively, you could use $\displaystyle \cos2\theta = 2\cos^2\theta - 1$

So $\displaystyle \cos2\theta = 0$

$\displaystyle \Rightarrow 2\theta = 90^o,\,270^o,\,450^o,\,630^o$

Then divide by $\displaystyle 2$.

Grandad