Question

If $n_{1}$ denotes the maximum number of roots of $\sin \theta=k_{1}$ in $[0,2 \pi]$ and $n_{2}$ denotes the maximum number of roots of $\cos \theta=k_{2}$ in $[0,2 \pi]$, then

• A. $n_{1}+n_{2}=5$
• B. $n_{1}+n_{2}=4$
• C. $n_{1}+n_{2}=6$
• D. $n_{1}+n_{2}=3$

Answer 1

Answer: (A)

$\sin \theta=k_{1}$ has maximum roots if $k_{1}=0$,
so $\theta=\pi, \pi, 2 \pi \cos \theta=k_{2}$ has maximum roots if $k_{2} \pi \pm 1$,
so there are two values of $\theta$.
$\therefore n_{1}=3$ and $n_{2}=2$