# Two geometry equations

• Mar 20th 2006, 01:04 AM
totalnewbie
Two geometry equations
How ?
• Mar 20th 2006, 02:43 PM
ThePerfectHacker
For Problem 1:
Factor to get, call $\displaystyle y=x-\frac{\pi}{5}$
$\displaystyle \cos y (2\cos^2y-3\cos y-1)=0$
Thus,
$\displaystyle \cos y=0$ or $\displaystyle 2\cos^2y-3\cos y-1=0$
$\displaystyle \cos y=\frac{3\pm\sqrt{17}}{4}$
Thus,
$\displaystyle \cos y=0$
$\displaystyle \cos y\approx 1.78$--Impossible.
$\displaystyle \cos y\approx -.28$
Solve for $\displaystyle y$
after that you can solve for $\displaystyle x$
• Mar 20th 2006, 02:49 PM
ThePerfectHacker
The product formula,
$\displaystyle \sin x\sin y=\frac{1}{2}[\cos(x-y)-\cos(x+y)]$
Thus,
$\displaystyle \sin (\pi/4+x)\sin (\pi/4-x)$
Can be expressed as,
$\displaystyle \frac{1}{2}[\cos(2x)-\cos(\pi/2)]$
But $\displaystyle \cos(\pi/2)=0$ thus,
$\displaystyle \frac{1}{2}\cos 2x=.33$
Thus,
$\displaystyle \cos 2x=.66$
Now you can solve for $\displaystyle 2x$ for which you can solve for $\displaystyle x$