William W. answered • 07/08/19
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Math and science made easy - learn from a retired engineer
The unit circle is great for understanding this.
Remember that sine = opp/hyp so (see above), so the sin(x) = opp/1. Can you see that the hypotenuse is the longest side of the triangle? It is 1 unit long. So the opposite side must be smaller than 1. That means opp/hyp must be < 1.
Same goes for cosine, cos(x) = adj/hyp and since the hyp is 1 and is the longest side of the triangle, the adjacent side must be smaller than 1 and then the cos(x) must be < 1
