How to use right triangles to evaluate the composition of a trig function and its inverse

The video tutorial explains the concept of cosine inverse, representing it as an angle, and how it relates to cosine. The instructor demonstrates how to use this understanding to draw a right triangle and calculate the tangent of the angle using the Pythagorean theorem. The process involves identifying the missing side of the triangle and using it to find the tangent, emphasizing the lack of restrictions in this context.

What does the cosine inverse of a number represent?

• A length of a side in a triangle

• A ratio of two sides in a triangle

• An angle

• A coordinate on the unit circle

If cosine inverse of 4/7 equals Theta, how can this be expressed using cosine?

• cosine of 4/7 equals Theta

• cosine of Theta equals 7/4

• cosine of Theta equals 4/7

• cosine of 7/4 equals Theta

In the context of a right triangle, what does the ratio 4/7 represent?

• The cosine of the angle

• The tangent of the angle

• The hypotenuse of the triangle

• The sine of the angle

What is the missing side of the triangle if the hypotenuse is 7 and one side is 4?

• 3

• sqrt(33)

• sqrt(21)

• 5

Why do we only consider the positive square root when solving for the missing side of the triangle?

• Because negative lengths are not possible

• Because the triangle is in the first quadrant

• Because the angle is acute

• Because the triangle is on the XY plane