Explaining hypotenuse the longest side using trig

1. Jun 19, 2013

needingtoknow

1. The problem statement, all variables and given/known data

I was just curious about something involving trig. How can sintheta <= 1. Shouldnt it be just sintheta < 1. By saying that its less or EQUAL to 1 does that not mean that the hypontenuse and the opposite side are equal, but the hypotenuse always has to be the longest side right. Isn't it impossible to draw a triangle where the hypotenuse is equal to another side? So how does that make sense trig wise?

2. Relevant equations

sintheta = opp/hyp

2. Jun 19, 2013

LCKurtz

That is what is sometimes called a "degenerate" triangle. One leg is 0 and the other leg and hypotenuse are equal. It happens when (x,y) = (0,1), (1,0),(0,-1), or (-1,0) when you draw the triangle on the unit circle.

3. Jun 19, 2013

needingtoknow

Oh great ok that makes sense then. Thanks!

4. Jun 19, 2013

HallsofIvy

Staff Emeritus
And, of course, trigonometry is not only used for right triangles. In fact, the main application of sine and cosine uses the fact that they are periodic. sin(x) and cos(x) are defied for all x. sin(x)= 0 for x any multiple of $\pi$, sin(x)= 1 for x any odd multiple of $\pi/2$.

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