Video narration
Does sin−1 mean one divided by sine? On your calculator, sine sends an angle to a value; inverse sine sends the value back to an angle. So sin−1(x), also called arcsin(x), means find the angle θ for which sin(θ)=x. It does not mean divide by sine. That reciprocal is cosecant, written csc. For example, sin(30°) equals 0.5, so sin−1(0.5) returns 30°-when the calculator is in degree mode. But sine values repeat: another angle can also produce 0.5. To return one dependable answer, inverse sine uses a principal range, from −90° to 90°. Its real inputs must stay between −1 and 1. The same reversal applies to inverse cosine and inverse tangent, each with its own chosen range. So, does sin−1 mean 1 over sine? No. It means the angle whose sine is that number. One over sine is cosecant.