Question

Which of the following are solutions to the equation sinxcosx = - 1/4

Answer 1

The equation is given below as

`\sin x\cos x=-(1)/(4)`

Recall that

`\begin{gathered} \sin 2x=2\sin xcosx \\ \text{which means that } \\ (\sin2x)/(2)=\sin x\cos x \end{gathered}`

Therefore, equating the two-equation, we will have

`(\sin 2x)/(2)=-(1)/(4)`

cross multiply, we will have

`\begin{gathered} \sin 2x=-(1)/(4)*2 \\ \sin 2x=-(1)/(2) \end{gathered}`

Therefore,

we will get the arc sign of both sides in radians to get

`\begin{gathered} 2x=\sin ^(-1)(-(1)/(2)) \\ x=(1)/(2)\sin ^(-1)(-(1)/(2)) \end{gathered}`

In radians, the final answer will be

`\begin{gathered} x=(7\pi)/(12)+n\pi \\ \text{and} \\ x=(11\pi)/(12)+n\pi \end{gathered}`

Therefore,

The finals answers are OPTION A and OPTION D