Question

If tan $\theta =\sqrt{2},$ then the value of $\theta$ is

• A. less than $\frac{\pi }{4}$
• B. equal to $\frac{\pi }{4}$
• C. between $\frac{\pi }{4}$ and $\frac{\pi }{3}$
• D. greater than $\frac{\pi }{3}$

Answer 1

The correct option is C between $\frac{\pi }{4}$ and $\frac{\pi }{3}$

$Giventan\theta =\sqrt{2}=1.414Toinvestigatewhether\theta isbetween\frac{\pi }{4}\&\frac{\pi }{3}Nowtan\frac{\pi }{4}=tan{45}^{\circ }=1$
When $\theta$ is between $0$ and $\frac{\pi }{2}$, $\tan \theta$, keeps on increasing.
$And,{tan\frac{\pi }{3}=tan60}^{\circ }=\sqrt{3}=1.732Also,giventhattan\theta =1.414So,clearly1.732>1.414>1So,\theta liesbetween\frac{\pi }{4}\&\frac{\pi }{3}$