Find the Exact Value of each expression (answer in Radians)

A) sin^-1(1/2)
B)cos^-1(1/2)

Question

Find the Exact Value of each expression (answer in Radians)

A) sin^-1(1/2)
B)cos^-1(1/2)

e.mccormick · Answer

Know your unit circle?

anonymous · Answer

I never learned it.

e.mccormick · Answer

OK.  Well, you need to work on that.  There is a way to remember it pretty easy using just the numbers 1, 2, and 3.  For now, just google one up to use.

If you think about it, $\sin^{-1}$ or arcsin and $\cos^{-1}$ or arccos have a very clear, reverse relationship to the non-arc versions.

e.mccormick · Answer

Lets say I have some angle, $\theta$ and from it I get a value through the use of cos.  That is an x value.

So $\cos\theta = x$

How do we get from x to $\theta$?  With arccos.

$\cos\theta = x$  Take the arccos of both sides:

$\arccos(\cos\theta) = \arccos (x)$  The arccos of cos cancels and:

$\theta = \arccos (x)$

So, if you have a unit circle, you can look for x=1/2 and what $\theta$ that works with.  Then look for y=1/2 for the arcsin one.