Question

If the point $(\cos \theta ,\sin \theta )$ does not fall in that angle between the lines $y=|x-1|$ in which the origin lies, then $\theta$ belongs to

• A. $(\frac{\pi }{2},\frac{3\pi }{2})$
• B. $(-\frac{\pi }{2},\frac{\pi }{2})$
• C. $(10,\pi )$
• D. None of these

Answer 1

The correct option is B $(-\frac{\pi }{2},\frac{\pi }{2})$

The lines are $y=x-1$ and $y=-x+1$ and $(\cos \theta ,\sin \theta )$ is any point on the circle $x^2+y^2=1$ whose centre is $(0,0)$ and radius is $1$.
Clearly from the figure, $\theta$ can vary from $-\frac{\pi }{2}$ to $\frac{\pi }{2}$.