Find all values of X in the interval [0,2pi]

sin 2= cosxx

Printable View

- Mar 15th 2013, 02:50 PMmlaschanskyNeed to find all values of X in the interval [0, 2pi]
Find all values of X in the interval [0,2pi]

sin 2= cos*x**x* - Mar 15th 2013, 02:58 PMProve ItRe: Need to find all values of X in the interval [0, 2pi]
I can't read your equation. Is it $\displaystyle \displaystyle \begin{align*} \sin{(2x)} = \sqrt{3}\,\cos{(x)} \end{align*}$?

- Mar 15th 2013, 04:39 PMHallsofIvyRe: Need to find all values of X in the interval [0, 2pi]
Assuming that it

**is**$\displaystyle sin(2x)= \sqrt{3}cos(x)$, use a trig identity: $\displaystyle sin(2x)= 2sin(x)cos(x)= \sqrt{3}cos(x)$ one solution is cos(x)= 0 which gives $\displaystyle x= \pi/2$. If cos(x) is NOT 0, we can divide both sides to get $\displaystyle 2sin(x)= \sqrt{3}$ so that $\displaystyle sin(x)= \frac{\sqrt{3}}{2}$. Can you solve that?