Question

which values are always less then 1

Answer 1

Negative values.

Answer 2

You mean which trig functions only give back values between -1 and 1, inclusive? Sine and cosine. Just look at the graphs of y = sin(x) and y = cos(x), and compare that to the graphs of the other trig functions.

Or to put it another way: think of the unit circle. Think of θ as the angle made with the vertex at (0,0), one end pointing at (1,0) and the other pointing at some point (x,y) on the unit circle. Project the point (x,y) on to the x-axis to make a right triangle. Then sin(θ) is opposite/hypotenuse = y / 1. You can't have y bigger than 1 or less than -1, because that would make it outside of the circle.

To put it an even simpler way for angles where 0 <= θ <= 90: the sine and cosine are each the lengths of some leg of the triangle over the hypotenuse. The hypotenuse is always the biggest side on a right triangle, so adjacent/hypotenuse and opposite/hypotenuse have to both be less than 1.

did this help?

Answer 3

no, i put exactly wat the question asked