 In this video, we provide the solution to question number three from practice final exam for math 1060 in which case we need to rewrite Cosine a sine inverse of x Using some equivalent algebraic form. So whenever you have these inverse trigonometric functions like this You want to think of it as an angle and you want to think of it as a right triangle diagram of some kind So if we have our right triangle like so again, this is a right triangle Really what we should be thinking of is that whenever you see this inverse trig function. It's an angle. So this is Theta, right? So theta equals sine inverse of x in particular I mean sine of theta equals x over 1 think of it as a ratio So we can label this triangle here where we have angle theta the sine ratio Just by basic so katala try triangle trigonometry. We get opposite over hypotenuse using the Pythagorean relationship We can figure out the other side is going to be the square root of 1 minus x squared And so now we're trying to compute cosine of theta, right? Cosine is going to be adjacent over hypotenuse. So we get the square root of 1 minus x squared over 1 Simplifying we see that the correct answer would be choice D