Trigonometric Functions and Identities

This video tutorial covers inverse trigonometric functions, focusing on inverse sine and cosine. It explains their ranges, properties, and how to use the unit circle for problem-solving. The tutorial also demonstrates using calculators to find inverse trigonometric values and solve equations. Real-world applications and graphing of these functions are discussed, providing a comprehensive understanding of inverse trigonometry.

Why do inverse sine and inverse cosine functions have different ranges?

• Because they have different periods.

• Because they are not one-to-one on the same interval.

• Because they are defined on different domains.

• Because they are not continuous functions.

What is the range of the inverse sine function?

• 0 to 2π

• -π/2 to π/2

• -π to π

• 0 to π

Which statement is true about the domain restriction of the sine function for its inverse to exist?

• It must be restricted to -π to π.

• It must be restricted to -π/2 to π/2.

• It must be restricted to 0 to 2π.

• It must be restricted to 0 to π.

What is the value of arc cosine of -1/2?

• π

• 2π/3

• π/3

• π/2

How do you verify the identity Arc cosine of -x equals π minus Arc cosine of x?

• By using the tangent function.

• By using the sine function.

• By using the Pythagorean theorem.

• By using the unit circle and specific values.

What is the angle in radians for arc tangent of 3?

• 1.25

• 0.71

• 0.93

• 1.41

Which trigonometric function is used to find an angle when given two legs of a right triangle?

• Secant

• Tangent

• Cosine

• Sine

In a right triangle, if the opposite side is 12 and the adjacent side is 5, what is the tangent of the angle?

• 5/13

• 13/5

• 5/12

• 12/5

What is the angle in radians that a 13-foot ladder makes with a building if it reaches a height of 12 feet?

• 0.56

• 1.25

• 1.11

• 0.395

If a ladder's angle of elevation must be between 35 and 45 degrees, does an angle of 60 degrees satisfy this requirement?

• It depends on the length of the ladder.

• No, it does not satisfy the requirement.

• It depends on the height of the building.

• Yes, it satisfies the requirement.