SOLUTION: what happens to sinθ as θ approaches 0 radians? Why?
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Question 1196692: what happens to sinθ as θ approaches 0 radians? Why?
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(53751) (Show Source): You can put this solution on YOUR website!
.
Then approaches to zero.
Why ? - - - because < .
Answer by MathLover1(20855) (Show Source): You can put this solution on YOUR website!
The way most people first encounter sine is as a ratio of two sides of a triangle.
In this case:
1. the sloping lines are all radii of the circle and represent the hypotenuse
2. the vertical lines are the ‘opposite’ side of the various triangles
As you can clearly see, as the angle reduces from
° → ° → ° → ° →° →° →° →°
the height of the vertical line (’opposite’) shrinks while the sloping line (‘hypotenuse’) remains constant
So the fraction opposite hypotenuse will, does and indeed to as reduces to .
The more modern way to define sine is with an infinite series:
+…....
....
But you can see how that also goes to zero as goes to zero!
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