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If sin=4/5 then that is cos =

 May 19, 2014

Best Answer 

 #5
avatar+26364 
+10

Hi Alan,

 

$$\\\cos{(\alpha)}=\textcolor[rgb]{1,0,0}{\pm}\frac{3}{5}\\
\text{if }{+\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(0.6) = 53.1301023542\ensuremath{^\circ}\\
\text{if }{-\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(-0.6) = 126.869897646\ensuremath{^\circ}\\
\sin{(53.1301023542\ensuremath{^\circ})}=\sin{(126.869897646\ensuremath{^\circ})}=0.8=\frac{4}{5}$$

Latex code:


\text{if }{+\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(0.6) = 53.1301023542\ensuremath{^\circ}\\
\text{if }{-\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(-0.6) = 126.869897646\ensuremath{^\circ}\\
\sin{(53.1301023542\ensuremath{^\circ})}=\sin{(126.869897646\ensuremath{^\circ})}=0.8=\frac{4}{5}

 May 20, 2014
 #1
avatar+128089 
0

Using the arcsin function

asin(4/5) = about 53.13 degrees

This angle could lie in the 2nd quadrant, too=  (180 - 53.13) = 126.87 degrees

 May 19, 2014
 #2
avatar+33603 
0

If sin=4/5 then we can picture the well known 3, 4, 5 right-angled triangle; so cos = 3/5.

 May 19, 2014
 #3
avatar+128089 
0

Thanks...alan....I've answered so many questions that I'm going snowblind!!!

 May 19, 2014
 #4
avatar+33603 
0

What, even with those shades!!!

 May 20, 2014
 #5
avatar+26364 
+10
Best Answer

Hi Alan,

 

$$\\\cos{(\alpha)}=\textcolor[rgb]{1,0,0}{\pm}\frac{3}{5}\\
\text{if }{+\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(0.6) = 53.1301023542\ensuremath{^\circ}\\
\text{if }{-\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(-0.6) = 126.869897646\ensuremath{^\circ}\\
\sin{(53.1301023542\ensuremath{^\circ})}=\sin{(126.869897646\ensuremath{^\circ})}=0.8=\frac{4}{5}$$

Latex code:


\text{if }{+\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(0.6) = 53.1301023542\ensuremath{^\circ}\\
\text{if }{-\frac{3}{5}} \Rightarrow \alpha = \cos^{-1}(-0.6) = 126.869897646\ensuremath{^\circ}\\
\sin{(53.1301023542\ensuremath{^\circ})}=\sin{(126.869897646\ensuremath{^\circ})}=0.8=\frac{4}{5}

heureka May 20, 2014
 #6
avatar+33603 
+5

You are right heureka;  sin is also positive in the second quadrant, where cos is negative.

 May 20, 2014

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