Question

the arcsin (- root 3/2) Find the exact value of the expression. (Enter your answers in radians.)

Answer 1

ask yourself if you know a number (angle) between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) whose sine is \(-\frac{\sqrt{3}}{2}\)

Answer 2

240 and 300

Answer 3

if that is not obvious look at the unit circle on the last page of the attached cheat sheet, and find the angles corresponding to the point where the second coordinate is \(-\frac{\sqrt{3}}{2}\)

Answer 4

it is neither of those
if you are working in degrees, you have to pick an angle between \(-90\) and \(90\)

Answer 5

4pi/3 ND 5PI/3

Answer 6

ok lets go slow
first of all it is only one number, not two
it is a well defined function, so there cannot be two answers, only one

Answer 7

ok

Answer 8

so 4pi/3

Answer 9

no you have to look on the right side of the unit circle for \(\sin^{-1}(x)\)

Answer 10

then 5pi/3?

Answer 11

now i see on the cheat sheet that the angle given on the right side is \(\frac{5\pi}{3}\) but that is not right either
it must be between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\)

Answer 12

so think of a negative angle that is coterminal with \(\frac{5\pi}{3}\)

Answer 13

the correct answer is \(-\frac{\pi}{3}\)

Answer 14

that is the only angle between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) whose sine is \(-\frac{\sqrt{3}}{2}\)

Answer 15

if you are working in degrees, it would be \(-60\)