Trigonometric Expressions and Functions

The video tutorial explains how to evaluate a trigonometric expression involving arctangent and express the result in terms of U, assuming U is positive. It begins by modeling the angle Theta on the coordinate plane, then calculates sin Theta using a reference triangle and the Pythagorean theorem. Finally, it demonstrates how to rationalize the expression, providing both simplified and rationalized forms.

What is the initial trigonometric expression that needs to be evaluated?

• T of arctangent U / 3

• C of arctangent U / 3

• S of arccosine U / 3

• S of arctangent U / 3

What assumption is made about U in the problem?

• U is negative

• U is zero

• U is positive

• U is a fraction

In which quadrant does the angle Theta terminate?

• First quadrant

• Fourth quadrant

• Third quadrant

• Second quadrant

What is the length of the opposite side of the reference triangle?

• 9

• 3

• U

• U/3

Which theorem is used to find the hypotenuse of the triangle?

• Tangent rule

• Pythagorean theorem

• Cosine rule

• Sine rule

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

• U + 9

• U^2 + 9

• Square root of (U^2 + 9)

• Square root of (U + 9)

What is the expression for sin Theta?

• U / square root of (U^2 + 9)

• 3 / square root of (U^2 + 9)

• 3 / U

• U / 3

What is the purpose of rationalizing the expression?

• To simplify the numerator

• To eliminate the square root from the denominator

• To change the expression to cosine

• To find the tangent of Theta

What do you multiply the numerator and denominator by to rationalize the expression?

• U

• 3

• Square root of (U^2 + 9)

• U^2 + 9

What is the final rationalized form of the expression?

• U * square root of (U^2 + 9) / (U^2 + 9)

• U / (U^2 + 9)

• 3 / (U^2 + 9)

• 3 * square root of (U^2 + 9) / U