trig equation

**blame_canada100** · October 6th 2009, 07:29 AM

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

2 cos^2 theta - 1=0

**Amer** · October 6th 2009, 10:13 AM

Originally Posted by blame_canada100

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

2 cos^2 theta - 1=0

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

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

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

theta equal the angle 45 in all quarters

**Grandad** · October 6th 2009, 12:37 PM

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 $\cos2\theta = 2\cos^2\theta - 1$

So $\cos2\theta = 0$

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

Then divide by $2$ .

Grandad

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