SOLUTION: why sin theta is equal to tan theta when angle is minimum

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Question 816261: why sin theta is equal to tan theta when angle is minimum
Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

why sin theta is equal to tan theta when angle is minimum

 tan = sin%28x%29+%2F+cos%28x%29  see graph: cos(0) = 1

 y = cos (x)

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
One way is:
For very thin right triangles, the adjacent side and the hypotenuse
are very nearly the same, so the opposite/hypotenuse is very close to
the opposite/adjacent.

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To elaborate on the other tutor's answer,

sin%28theta%29%2Fcos%28theta%29 = tan%28theta%29

Multiply both sides by cos%28theta%29

sin%28theta%29 = tan%28theta%29cos%28theta%29

Divide both sides by tan%28theta%29


sin%28theta%29%2Ftan%28theta%29 = cos%28theta%29

When theta is very near to zero, the right side cos%28theta%29 is 
very near to 1, since cos%280%29 = 1

so the ratio of the sine to the tangent is very near to 1, which means
they are nearly equal.

Edwin