Question

Find all solutions in the interval [0, 2π). (sin x)(cos x) = 0

Answer 1

Answer:

The solution in the interval [0, 2π) of the expression $(\sin x)(\cos x) = 0$ are $x=0,\pi,\frac{\pi}{2},\frac{3\pi}{2}$                                

Step-by-step explanation:

Given : Expression $(\sin x)(\cos x) = 0$

To find : All the solutions in the interval [0, 2π) ?

Solution :

Expression $(\sin x)(\cos x) = 0$

When $a\cdot b=0\Rightarrow a=0\text{ or } b=0$

$\sin x= 0$  or $\cos x= 0$      

$x=\sin^{-1}(0)$  or $x=\cos^{-1}(0)$        

The general solution of the equations are

$x=0,\pi,2\pi,..$  or $x=\frac{\pi}{2},\frac{3\pi}{2},..$

From $0\leq x$

The solutions are          

$x=0,\pi$  or $x=\frac{\pi}{2},\frac{3\pi}{2}$    

Therefore, The solution in the interval [0, 2π) of the expression $(\sin x)(\cos x) = 0$ are $x=0,\pi,\frac{\pi}{2},\frac{3\pi}{2}$  

Answer 2

$\bf sin(x)cos(x)=0\implies \begin{cases} sin(x)=0\\ \measuredangle x=sin^{-1}(0)\\ \measuredangle x=0\ ,\ \pi \\ ----------\\ cos(x)=0\\ \measuredangle x=cos^{-1}(0)\\ \measuredangle x=\frac{\pi }{2}\ ,\ \frac{3\pi }{2} \end{cases}$