1. ## Analytic Trig

Solve each equation on the interval 0 greater than or equal to theta or less than 2pie.

12) 4 (cos^2) theta - 3 = 0

Please be descriptive I have having difficulties with these types. TY

2. Originally Posted by kukid123
Solve each equation on the interval 0 greater than or equal to theta or less than 2pie.

12) 4 (cos^2) theta - 3 = 0

Please be descriptive I have having difficulties with these types. TY
Just "unwrap" it like you would any other equation.

$\displaystyle 4\cos^2{\theta} - 3 = 0$ Add 3 to both sides.

$\displaystyle 4\cos^2{\theta} = 3$ Divide by 4.

$\displaystyle \cos^2{\theta} = \frac{3}{4}$. Take the square root.

$\displaystyle \cos{\theta} = \pm\frac{\sqrt{3}}{2}$.

So what values of $\displaystyle \theta$ make $\displaystyle \cos{\theta} = \frac{\sqrt{3}}{2}$ or $\displaystyle -\frac{\sqrt{3}}{2}$.

We know $\displaystyle \cos{\frac{\pi}{6}} = \frac{\sqrt{3}}{2}$

So $\displaystyle \frac{\pi}{6}$ is the focus angle.

In the domain $\displaystyle 0 \leq x \leq 2\pi$ the solutions are...

$\displaystyle x = \left\{\frac{\pi}{6}, \pi - \frac{\pi}{6}, \pi + \frac{\pi}{6}, 2\pi - \frac{\pi}{6}\right\}$

$\displaystyle = \left\{\frac{\pi}{6}, \frac{5\pi}{6}, \frac{7\pi}{6}, \frac{11\pi}{6}\right\}$.

Does that make sense?

3. Yeah thanks bro. Great work.