You are asked to find the inverse sine of 2/3 (or `sin^(-1)(2/3) ` ), also called the arcsin.
There are a couple of things you need to know to answer correctly on a computer:
(1) Your answer is correct if the answer is supposed to be in degrees.
(a) Check if your answer is supposed to be in radians. If so, change the mode of your calculator to radian mode to get `sin^(-1)(2/3)~~0.7297276562 `
(b) If the answer was supposed to be in degrees, check the instructions for the degree of accuracy. If you are supposed to answer to the nearest degree the answer is 42 degrees; to the nearest tenth of a degree it should be 41.8 degrees, etc...
(2) If the answer is supposed to be in radians, you need to check to see the precision of the answer. Usually this is to 4 decimal places, so the answer would be 0.7297 radians. (The program might insist that the leading zero is there, or might not want the leading zero -- you will want to check the instructions.)