Question

Which of the following are solutions to the equation sinx cosx = S? Check all that apply. . 13. 51 12 . c.플 EN D. + 12

Answer 1

Answer

$x=\frac{\pi}{12}+n\pi.\text{ Option D is correct.}$

Explanations:

Given the trigonometry equation expressed as;

$sinxcosx=\frac{1}{4}$

We are to simplify for the value(s) of 'x"

Recall from trigonometry identity that:

$\begin{gathered} Sin2x=2sinxcosx \\ sinxcosx=\frac{sin2x}{2} \end{gathered}$

Substitute the result into the original equation to have:

$\begin{gathered} \frac{sin2x}{2}=\frac{1}{4} \\ sin2x=\frac{1}{2} \end{gathered}$

Solve for the value of "x"

$\begin{gathered} 2x=sin^{-1}(\frac{1}{2}) \\ 2x=30^0 \\ x=\frac{30}{2} \\ x=15 \\ x=\frac{\pi}{12} \\ \end{gathered}$

The general solution to the given trigonometry function is:

$x=\frac{\pi}{12}+n\pi$