Evaluating the composition of Functions using Right Triangles

The video tutorial explains how to evaluate the cosine of the arcsine of 2X. It begins by introducing the problem and the need to construct a triangle to find the angle whose sine is 2X. The tutorial discusses the selection of the correct triangle based on the range of the inverse sine function. It then derives the formula for the adjacent side of the triangle and uses it to determine the cosine. The final solution is presented as the cosine of the angle, calculated as the adjacent side over the hypotenuse.

What is the main goal when evaluating the cosine of arcsine of 2X?

• To find the angle whose cosine is 2X

• To find the angle whose tangent is 2X

• To find the angle whose cotangent is 2X

• To find the angle whose sine is 2X

Why is only one triangle used in the evaluation process?

• Because the inverse sine function has a limited range

• Because the inverse cosine function has a limited range

• Because the inverse tangent function has a limited range

• Because the inverse cotangent function has a limited range

What is the formula used to find the adjacent side of the triangle?

• Adjacent squared equals 4X squared plus 1

• Adjacent squared equals 4X squared minus 1

• Adjacent squared equals 1 plus 4X squared

• Adjacent squared equals 1 minus 4X squared

In which quadrant is the adjacent side of the triangle located?

• Fourth quadrant

• First quadrant

• Second quadrant

• Third quadrant

How is the cosine of the angle determined in the final step?

• By dividing the hypotenuse by the adjacent side

• By dividing the hypotenuse by the opposite side

• By dividing the opposite side by the hypotenuse

• By dividing the adjacent side by the hypotenuse