Question

Refer to the appropriate triangle or trigonometric identity to compute:
cos(sin^-1(2/3))

Answer 1

To start off with, if sin^-1(2/3) = theta, then sin(theta) = 2/3. This can then be visually shown with a triangle.

Answer 2

considering that sin represents the opposite side of a triangle over the hypotenuse, I can show this relationship like this.

Answer 3

From there, we want the cosine, which we can derive from this triangle using the pythagorean theorem. If a^2 + b^2 = c^2, I can then say that a^2 = c^2 - b^2 and solve for a. Once you get that value, remember that cosine refers to the adjacent side of a triangle over the hypotenuse. I'll let ya finish the problem from there, as to not do it all for ya ^_^

Answer 4

Thanks so much! I appreciate it :)

Answer 5

glad to help ^_^