Evaluate the expression. cos ( sin − 1 1 ) \cos\left(\sin^{-1}1\right) cos ( sin − 1 1 )

this problem, we're asked to evaluate the expression that the cosine of the inverse sine of 1. Now, because this is a composite function, we know that we want to look at that inside function first, which is the inverse sine of 1. Now, when working with inverse trig functions, we also know that we can think of this as, okay, the sine of what angle is equal to 1. Now, again, because this is an inverse trig function, we also know that we are only looking at angles within a specific interval. So for the inverse sine, we only want to look at angles between negative pi over 2 and positive pi over 2, so only on this half of my unit circle. I want to find the angle for which the sine is equal to 1 in this interval, which is pi over 2. So the sine of pi over 2 is equal to 1. So that tells me that my answer to this inside function is pi over 2. Now that I have that information, I'm just left to find the cosine of that angle, pi over 2, which is 0. So that gives me my final answer. The cosine of the inverse sine of 1 is equal to 0. Thanks for watching, and let me know if you have questions.