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. $(0,\pi )$
• D. none of these

Answer 1

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

Clearly, the point $(\cos \theta ,\sin \theta )$ lie on the circle

The two lines represented by the equation $y=|x-1|$ are $y=x-1$ and $y=1-x$

From figure $\theta$ can vary from $-\frac{\pi }{2}$ to $\frac{\pi }{2}$