How to evaluate the difference of two angles for tangent, tan

The video tutorial explains how to evaluate the tangent of 165 degrees by rewriting it as the difference of tangents of 210 and 45 degrees. The instructor provides a formula for tangent difference and demonstrates how to plug in angles and simplify the expression. The tutorial covers evaluating tangent using sine and cosine coordinates, rationalizing denominators, and multiplying by the conjugate to simplify expressions. The final result is a simplified exact answer for the tangent of 165 degrees.

What is the formula for tangent of U - V?

• tangent U * tangent V / 1 - tangent U + tangent V

• tangent U - tangent V / 1 + tangent U * tangent V

• tangent U + tangent V / 1 - tangent U * tangent V

• tangent U / tangent V + 1 - tangent U * tangent V

How is the tangent of 210 degrees calculated using sine and cosine?

• By dividing the Y coordinate by the X coordinate

• By dividing the X coordinate by the Y coordinate

• By subtracting the X coordinate from the Y coordinate

• By adding the Y and X coordinates

What is the result of rationalizing the denominator for tangent 210 degrees?

• 3 / sqrt 3

• sqrt 3 / 3

• 1

• sqrt 3

Why is it important to rationalize the denominator in tangent calculations?

• To change the angle of the tangent

• To make the expression more complex

• To increase the value of the expression

• To simplify the expression for an exact answer

What is the purpose of multiplying by the conjugate in simplifying expressions?

• To add more terms to the expression

• To eliminate radicals from the denominator

• To increase the numerator value

• To change the sign of the expression

What method is used to multiply binomials in the final simplification?

• The division method

• The subtraction method

• The addition method

• The box method

What is the final exact answer for the tangent evaluation?

• 2 - sqrt 3

• 2 + sqrt 3

• sqrt 3 - 2

• sqrt 3 + 2