Trigonometric Inequality

Positive and Negative Angles:

Variations of sin θ, cos θ, tan θ:

By definition we have, sin θ =  and cos θ = 

As – r ≤ y ≤ r ⇒ -l ≤ y/r ≤ l ⇒ -1 ≤ sin θ ≤ l

as – r ≤ x ≤ r ⇒ -1 ≤ x/r ≤ 1 ⇒ -1 ≤ cos θ ≤ 1

as tan θ = y/x ⇒ -∞ < tan θ < ∞

In general we can say that:

sin θ and cos θ can never be greater than 1 or less than -1.

sec θ and cosec θ can never be between -1 and +1.

tan θ and cot θ can take any positive or negative value.