Sine Cosine and Tangent

Question

Why can sine and cosine never be greater than ? Why is it that cosecant and secant should be greater than ? Why are tangent and cotangent sometimes undefined?

Answer 1

Hi Alyssa,

If you draw a right triangle with the opposite o, adjacent a, and hypotenuse h, sides then for any angle the sine is o/h but h=(o²+a²)^.5, so the sine =o/(o²+a²)^.5 which is clearly less than or equal to 1. Similar argument for the cos ie it' s a/h.

Cosecant =1/sine so any time the sine is less than 1 the cosecant is greater than one Similar arguement for the secant=1/cosine.

If you look a the the definitions of the trig functions in terms of angles these questions are easier to answer.

Regards

Jim