Question

Find the exact value of arccos (sin (pi/6). Explain your reasoning.

Answer 1

\[\large \arccos\left[\color{royalblue}{\sin\left(\frac{\pi}{6}\right)}\right]\]Work from the inside out, so start with the blue part. Do you remember what sin pi/6 gives you?

Answer 2

i'd help , but math is like a different language for me lol

Answer 3

From our special triangles and trig ratios, we know that sin(pi/6) = 1/2
So now we can replace sin(pi/6) with 1/2. Now it looks something like this:

\[\arccos\left[ \frac{ 1 }{ 2 } \right]\]

Since arccos is the inverse function of cosine, then originally, if that question was cos(1/2), we 1/2 would be the x value, and we would need to find the y value when x is 1/2. But since arccos is the inverse of cosine, then their domain and range switch. So now I'm finding x when y = 1/2. It's the same as saying cos(y) = 1/2 At what value of y is cosine 1/2? From what we know it's pi/3.

Thus, arccos(1/2) = pi/3

Answer 4

\[\cos^{-1} (\sin \frac{\pi}{6})=\cos^{-1} (\frac{1}{2}=\frac{\pi}{3}\]