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Why is the sine of 90 degrees equal to 1?

 Jun 26, 2014

Best Answer 

 #1
avatar+576 
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There are a handful of reasons.  Let's start with a relatively basic one and see where the conversation goes.  In geometry we learn that the sine ratio is equal to the ratio of the lengths of the opposide side and hypotenuse of a right triangle.  Let's apply this to an arbitrary right triangle.  When we select the right angle as our angle for the sine function something odd happens.  It turns out that the opposite side, in this case, is the hypotenuse!

sin(90)=o/h

o=h

Therefore o/h=1

 

If you make it a little bit farther in math you could consider the unit circle.  On the unit circle 90 degrees represents a vector of magnitude 1 pointing straight up from the origin to the point (0,1).  Since sin(x)=y it follows by substitution that since y=1, sin(90)=1

 Jun 26, 2014
 #1
avatar+576 
+5
Best Answer

There are a handful of reasons.  Let's start with a relatively basic one and see where the conversation goes.  In geometry we learn that the sine ratio is equal to the ratio of the lengths of the opposide side and hypotenuse of a right triangle.  Let's apply this to an arbitrary right triangle.  When we select the right angle as our angle for the sine function something odd happens.  It turns out that the opposite side, in this case, is the hypotenuse!

sin(90)=o/h

o=h

Therefore o/h=1

 

If you make it a little bit farther in math you could consider the unit circle.  On the unit circle 90 degrees represents a vector of magnitude 1 pointing straight up from the origin to the point (0,1).  Since sin(x)=y it follows by substitution that since y=1, sin(90)=1

jboy314 Jun 26, 2014

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