find the exact value without a calculator. arccos(sin(π/6)) arccos(sin(π/6)) = □ (simplify your answer. type…

find the exact value without a calculator. arccos(sin(π/6)) arccos(sin(π/6)) = □ (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

find the exact value without a calculator. arccos(sin(π/6)) arccos(sin(π/6)) = □ (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression.)

Answer

Answer:

$\frac{\pi}{3}$

Explanation:

Step1: Find $\sin(\frac{\pi}{6})$ value

We know that $\sin(\frac{\pi}{6})=\frac{1}{2}$.

Step2: Calculate $\arccos(\frac{1}{2})$

Let $y = \arccos(x)$, where $x=\frac{1}{2}$ and the range of $y$ for $y=\arccos(x)$ is $[0,\pi]$. We know that $\cos y=x$, so $\cos y=\frac{1}{2}$ and in the range $[0,\pi]$, $y = \frac{\pi}{3}$.