Inverse Trigonometric Functions Concepts

This video tutorial introduces inverse functions for sine, cosine, and tangent. It explains how to restrict domains to make these functions one-to-one, allowing for the determination of their inverses. The video covers the graphing of inverse functions and demonstrates how to use them to solve trigonometric problems, including solving right triangles using the Pythagorean theorem and inverse tangent calculations.

Why do sine, cosine, and tangent functions need domain restrictions to have inverses?

• They are not continuous functions.

• They are not one-to-one functions.

• They are not differentiable.

• They do not have a range.

What is the range of the inverse sine function?

• 0 to π

• 0 to 2π

• -π/2 to π/2

• -1 to 1

Which of the following is a correct representation of the inverse sine function?

• y = arcsin(x)

• y = cos(x)

• y = arccos(x)

• y = sin(x)

What is the domain of the inverse cosine function?

• -1 to 1

• 0 to π

• 0 to 2π

• -π/2 to π/2

How is the inverse cosine function denoted?

• y = cos(x)

• y = arctan(x)

• y = arccos(x)

• y = tan(x)

What is the range of the inverse tangent function?

• 0 to 2π

• -1 to 1

• 0 to π

• -π/2 to π/2

Which of the following is a correct representation of the inverse tangent function?

• y = arcsin(x)

• y = sin(x)

• y = arctan(x)

• y = tan(x)

In solving problems with inverse trig functions, what is the significance of reference triangles?

• They are used to calculate the area of a triangle.

• They are used to find the hypotenuse.

• They help in determining the exact angle values.

• They are used to determine the perimeter of a triangle.

What is the inverse tangent of 1?

• π/4

• 0

• π/2

• -π/4

When solving a right triangle, why is it important to use inverse trigonometric functions?

• To find the length of the hypotenuse.

• To determine the measure of angles accurately.

• To calculate the area of the triangle.

• To find the perimeter of the triangle.