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how do you use cos-1

 Feb 13, 2015

Best Answer 

 #1
avatar+5479 
+26

While the cosine of a given angle is used to find the ratio of its opposite side / hypotenuse, the arccosine does the opposite: it finds the measure of an angle from the given ratio of its opposite side / hypotenuse.

 

For example,  $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)} = {\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}$$

 

So $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}\right)} = {\mathtt{45}}$$

 

So if you had the lengths of the opposite side and the hypotenuse for a right triangle, you would use arccosine to find the measure of the angle.

 Feb 13, 2015
 #1
avatar+5479 
+26
Best Answer

While the cosine of a given angle is used to find the ratio of its opposite side / hypotenuse, the arccosine does the opposite: it finds the measure of an angle from the given ratio of its opposite side / hypotenuse.

 

For example,  $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)} = {\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}$$

 

So $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}\right)} = {\mathtt{45}}$$

 

So if you had the lengths of the opposite side and the hypotenuse for a right triangle, you would use arccosine to find the measure of the angle.

kitty<3 Feb 13, 2015
 #2
avatar+112861 
+5

Inverse cos is the same as arccos

On this calc you use acos

 Feb 13, 2015

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