Can there ever be a trigonometric ratio larger than one?

Question

aaronandyson · Answer

What trigonometric ratio are you talking about?

math_genius12345 · Answer

@AaronAndyson I'm doing a project based on this question and I don't quite understand it either. The question is this: 

Can we ever have a trigonometric ratio larger than one? Why or why not?

I'm supposed to answer for each sine, cosine, and tangent.

aaronandyson · Answer

Please post a screenshot of the original question.

imqwerty · Answer

yes some trigonometric ratios can be greater than one

hint:think about tan$\theta$

math_genius12345 · Answer

Here's the instructions:
You have learned about the three basic trigonometric ratios: sine, cosine, and tangent. We learn this in geometry with reference to right triangles. What patterns have you found with these three ratios? Do you think we can limit any values for sine, cosine, and tangent? Or are these unbounded and can go to infinity (and beyond!)?

aaronandyson · Answer

First,
Draw an unit circle.

zepdrix · Answer

If you think of sine and cosine in terms of a triangle|dw:1470076440500:dw|sine is defined as the ratio of the opposite to the hypotenuse.
If this ratio is greater than 1, it means the numerator (opposite) is longer than the hypotenuse.

This cannot happen in a right triangle, ya?
The hypotenuse must be the longest side.