Trigonometric Functions and Their Applications

The video tutorial explains how to evaluate the sine of the inverse tangent of U divided by 3, given that U is positive. It introduces angle A, whose tangent is U/3, and constructs a reference triangle in the first quadrant. Using the Pythagorean theorem, the hypotenuse is calculated, allowing the determination of the sine of angle A. The sine is expressed as a ratio and rationalized for clarity.

What is the initial problem we are trying to solve in this tutorial?

• Evaluate the sine of inverse tangent of U divided by 3.

• Evaluate the sine of inverse cosine of U divided by 3.

• Evaluate the tangent of inverse sine of U divided by 3.

• Evaluate the cosine of inverse tangent of U divided by 3.

What does the inverse tangent of U/3 represent in terms of angle A?

• Angle A has a cosine function value of U divided by 3.

• Angle A has a cotangent function value of U divided by 3.

• Angle A has a sine function value of U divided by 3.

• Angle A has a tangent function value of U divided by 3.

In which quadrant is angle A located, given that U is positive?

• Fourth quadrant

• First quadrant

• Third quadrant

• Second quadrant

What are the lengths of the opposite and adjacent sides in the reference triangle for angle A?

• Opposite: 3, Adjacent: 3

• Opposite: U, Adjacent: U

• Opposite: U, Adjacent: 3

• Opposite: 3, Adjacent: U

Which theorem is used to determine the length of the hypotenuse in the reference triangle?

• Tangent Rule

• Pythagorean Theorem

• Cosine Rule

• Sine Rule

What is the expression for the hypotenuse length in terms of U?

• Square root of U + 3

• Square root of U + 9

• Square root of U squared + 9

• Square root of U squared + 3

How is the sine of angle A calculated from the reference triangle?

• Ratio of opposite side to hypotenuse

• Ratio of hypotenuse to opposite side

• Ratio of hypotenuse to adjacent side

• Ratio of adjacent side to hypotenuse

What is the rationalized form of the sine of angle A?

• U divided by the square root of U squared + 9

• U times the square root of U squared + 9 divided by U squared + 9

• U divided by U squared + 9

• U times the square root of U squared + 3 divided by U squared + 3

What is the purpose of rationalizing the expression for the sine of angle A?

• To change the expression to a cosine function

• To make the expression more complex

• To convert the expression to a tangent function

• To simplify the expression

What is the final simplified trigonometric expression for the sine of angle A?

• U times the square root of U squared + 9 divided by U squared + 9

• U divided by the square root of U squared + 9

• U divided by U squared + 9

• U times the square root of U squared + 3 divided by U squared + 3