Question

Find the exact value of each real number y if it exists. How do I solve without using a calculator?

y=arcsin (- square root of 3/2)

Answer 1

on the unit circle there are 2 places where the sin is -sq rt 3/2. Those two places are at \[\frac{ 4\pi }{ 3 },\frac{ 5\pi }{ 3 }\]These are in the third and fourth quadrants, respectively. The rotation for the point in the third quadrant is \[\frac{ 4\pi }{ 3 }\]plus any multiple of 2pi. the rotation for the point in the fourth quadrant is \[\frac{ 5\pi }{ 3 }\]plus and multiple of 2pi. So all the values for arcin(-sqrt3/2) are\[\frac{ 4\pi }{ 3 }+2k \pi \]and \[\frac{ 5\pi }{ 3 }+2k \pi \], k an integer.

Answer 2

Seems a bit vague and tedious but they are inverses and somewhat ambiguous to begin with. But that's your answer.

Answer 3

The answer for this problem in the textbook is -pi/3. Initially I was going the route to you have explained but the answer just confused me. Any thoughts?

Answer 4

You can say this:
\[\frac{5\pi}{3}=-\frac{\pi}{3}\]

Answer 5

Thanks for that explanation...I was away watching some crazy binomial expansion somewhere else...