find a value of x that satisfies the following statement.\n\n\\( \\sin x = \\cos \\frac { 5 \\pi } { 12 }…

find a value of x that satisfies the following statement.\n\n\\( \\sin x = \\cos \\frac { 5 \\pi } { 12 } \\)\n\nchoose the value of x that satisfies the statement.\n\n\\( \\bigcirc \\) a. \\( x = \\frac { \\pi } { 6 } \\)\n\\( \\bigcirc \\) b. \\( x = \\frac { \\pi } { 24 } \\)\n\\( \\bigcirc \\) c. \\( x = \\frac { \\pi } { 12 } \\)\n\\( \\bigcirc \\) d. \\( x = - \\frac { \\pi } { 12 } \\)

find a value of x that satisfies the following statement.\n\n\\( \\sin x = \\cos \\frac { 5 \\pi } { 12 } \\)\n\nchoose the value of x that satisfies the statement.\n\n\\( \\bigcirc \\) a. \\( x = \\frac { \\pi } { 6 } \\)\n\\( \\bigcirc \\) b. \\( x = \\frac { \\pi } { 24 } \\)\n\\( \\bigcirc \\) c. \\( x = \\frac { \\pi } { 12 } \\)\n\\( \\bigcirc \\) d. \\( x = - \\frac { \\pi } { 12 } \\)

Answer

Explanation:

Step1: Use co - function identity

We know that (\sin x=\cos\left(\frac{\pi}{2}-x\right)). Given (\sin x = \cos\frac{5\pi}{12}), then (\cos\left(\frac{\pi}{2}-x\right)=\cos\frac{5\pi}{12}).

Step2: Solve for (x)

If (\cos A=\cos B), then (A = 2k\pi\pm B,k\in\mathbb{Z}). Taking (k = 0) and the positive case (A = B), we have (\frac{\pi}{2}-x=\frac{5\pi}{12}). [ \begin{align*} -x&=\frac{5\pi}{12}-\frac{\pi}{2}\ -x&=\frac{5\pi}{12}-\frac{6\pi}{12}\ -x&=-\frac{\pi}{12}\ x&=\frac{\pi}{12} \end{align*} ]

Answer:

C. (x = \frac{\pi}{12})