Question

In a right angled triangle, the hypotenuse is the largest side and thus, the value of $\sin \theta$ or $\cos \theta$ is

• A. $>1$
• B. $=1$
• C. $\ge 1$
• D. $<1$

Answer 1

The correct option is D $<1$


In a right angled triangle, the hypotenuse is the largest side and thus the value of $\sin \theta$ and $\cos \theta$ is always less than $1$ or at the most equal to $1$.
$\sin \theta =\frac{perpendicular}{hypotenuse}and\cos \theta =\frac{base}{hypotenuse}$

$perpendicular<hypotenuse\Rightarrow \frac{perpendicular}{hypotenuse}<1\Rightarrow \sin \theta <1$

$base<hypotenuse\Rightarrow \frac{base}{hypotenuse}<1\Rightarrow \cos \theta <1$