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 #2
avatar+118724 
+5
May 16, 2014
 #5
avatar+118724 
0
May 16, 2014
 #2
avatar+118724 
+10

Maybe this site will help

http://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html

Remember, with the unit circle cos x is given by the x value and sinx is given by the y value - this is because the hypotenuse is 1 at all times.

Look at the interactive picture and see if you can comprehend what I am tlaking about and why it it so!

If you understand the unit circle properly it will make much of trig a lot easier to understand and remember.

May 16, 2014
 #2
avatar+118724 
0
May 16, 2014
 #4
avatar+26400 
+5

...continued.

if x is in degrees:

$$\\cos(x) = cos\left[180\textcolor[rgb]{1,0,0}{\ensuremath{^\circ}}-cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\right]
\quad | \quad \pm cos^{-1}\\
\pm x=\pm \left[ 180\ensuremath{^\circ}} -cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\right]\\
x=180\ensuremath{^\circ}} -cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\\
cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\right]=180\ensuremath{^\circ}}-x
\quad | \quad \cos{}\\\\
\frac{0.25}{6,76}*\cos{(x)}=\cos{(180\ensuremath{^\circ}}-x)}\\
\frac{0.25}{6,76}*\cos{(x)}=\underbrace{\cos{180\ensuremath{^\circ}}}_{-1}\cos{(x)}
+\underbrace{\sin{180\ensuremath{^\circ}}}_{0}\sin{(x)}\\
\frac{0.25}{6,76}*\cos{(x)}=-\cos{(x)}\\
\frac{0.25}{6,76}*\cos{(x)}+\cos{(x)}=0\\
\cos{(x)}\left(\frac{0.25}{6,76}+1\right)=0\\
\cos{(x)}=0\quad | \quad \pm \cos^{-1}\\
\pm x=\frac{\pi}{2}\\\\
\boxed{x=\frac{\pi}{2} \pm 2\pi*k\qquad or \qquad x=-\frac{\pi}{2} \pm 2\pi*k}$$

\\cos(x) = cos\left[180\textcolor[rgb]{1,0,0}{\ensuremath{^\circ}}-cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\right]
\quad | \quad \pm cos^{-1}\\
\pm x=\pm \left[ 180\ensuremath{^\circ}} -cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\right]\\
x=180\ensuremath{^\circ}} -cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\\
cos^{-1}(\frac{0.25}{6,76}*\cos{(x)})\right]=180\ensuremath{^\circ}}-x
\quad | \quad \cos{}\\\\
\frac{0.25}{6,76}*\cos{(x)}=\cos{(180\ensuremath{^\circ}}-x)}\\
\frac{0.25}{6,76}*\cos{(x)}=\underbrace{\cos{180\ensuremath{^\circ}}}_{-1}\cos{(x)}
+\underbrace{\sin{180\ensuremath{^\circ}}}_{0}\sin{(x)}\\
\frac{0.25}{6,76}*\cos{(x)}=-\cos{(x)}\\
\frac{0.25}{6,76}*\cos{(x)}+\cos{(x)}=0\\
\cos{(x)}\left(\frac{0.25}{6,76}+1\right)=0\\
\cos{(x)}=0\quad | \quad  \pm \cos^{-1}\\
\pm x=\frac{\pi}{2}\\\\
\boxed{x=\frac{\pi}{2} \pm 2\pi*k\qquad or \qquad x=-\frac{\pi}{2} \pm 2\pi*k}




May 16, 2014
 #1
avatar+130518 
+8
May 16, 2014

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