So I understand problem 55 up until you come out with sin x = {3/4, 1/3}. However, I simply did arcsin(3/4) and arcsin(1/3) and came out with x?{.8481,.3398}. However, the book showed two other answers that I should get, and I understand that they are also points on the arcsin graphs. However, I don't understand why we use two of them on each graph. Shouldn't the arcsin function only have one value for x? And even if it did use more than the one, then how would I know which to use when there are infinite points on the arcsin graph? Furthermore, how would I calculate the other value? It gives ~2.2935 as one of the values, and if I enter in sin(2.2935), i get ~.75. But I don't know how to find that without having it in the book. Thanks!
-Molly
Great question, Molly! I've posted it here on the blog because I think others may be interested in the answer.
ReplyDeleteYou are correct that the arcsine function only has one answer. However, the sine function has an infinite set of angles that give 0.75. To find the others, you need to not only consider all the angles coterminal to the angles you found, but also the angles in the second quadrant with that same reference angle- i.e. π - arcsin(3/4) and π - arcsin(1/3) and all their coterminal angles.
Let me know if that helps!