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.

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CCSS.HSF-BF.B.4D

What is the range of the inverse sine function?

• 0 to 2π

• -π/2 to π/2

• -π to π

• 0 to π

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CCSS.HSF-BF.B.4D

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.

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CCSS.HSF.TF.B.7

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

• π

• 2π/3

• π/3

• π/2

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CCSS.HSF.TF.C.8

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.

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CCSS.HSF.TF.B.7

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

• 1.25

• 0.71

• 0.93

• 1.41

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CCSS.HSG.SRT.C.6

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

• Secant

• Tangent

• Cosine

• Sine

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CCSS.HSG.SRT.C.6

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

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CCSS.HSG.SRT.C.8

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

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CCSS.8.G.A.5

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.

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CCSS.8.G.A.5