Evaluating the composition of Functions using Right Triangles

The video tutorial explains how to evaluate the sine of the inverse cosine of sqrt(5)/5 by constructing a right triangle. It discusses the properties of inverse cosine, the creation of possible triangles, and the selection of the valid triangle in the first quadrant. The Pythagorean theorem is used to find the opposite side, leading to the final calculation of the sine value.

What does the inverse cosine function represent in a right triangle?

• The ratio of the opposite side to the hypotenuse

• The ratio of the adjacent side to the hypotenuse

• The ratio of the opposite side to the adjacent side

• The ratio of the hypotenuse to the adjacent side

Why is only one triangle valid for the inverse cosine of square root 5 over 5?

• Because it must be in the fourth quadrant

• Because it must be in the first or second quadrant

• Because it must be in the third quadrant

• Because it must be in the second or third quadrant

Which theorem is used to find the length of the opposite side in the triangle?

• Pythagorean Theorem

• Cosine Rule

• Quadratic Formula

• Sine Rule

What is the value of the opposite side when using the Pythagorean theorem in this context?

• 5

• Square root of 20

• Square root of 5

• 2 times the square root of 5

What is the final value of the sine of the angle in the triangle?

• Square root of 5 over 5

• 2 times the square root of 5 over 5

• 5 over square root of 5

• Square root of 5 over 2