Understanding Tangent Pi Over 12 Using Sum and Difference Identities

The video tutorial explains how to determine the exact trigonometric function value of tangent pi over 12 radians using the sum and difference identity. It begins by converting radians to degrees and selecting angles with known trigonometric values. The tutorial then applies the tangent formula, evaluates the trigonometric functions, and rationalizes the denominator to find the exact value of tangent 15 degrees.

What is the main goal of the problem discussed in the video?

• To determine the exact value of tangent pi over 12 radians

• To convert pi over 12 radians to degrees

• To calculate the cosine of pi over 12 radians

• To find the sine of pi over 12 radians

What is the degree equivalent of pi over 12 radians?

• 15 degrees

• 45 degrees

• 60 degrees

• 30 degrees

Which pair of angles is chosen to simplify the calculation of tangent 15 degrees?

• 45 degrees and 30 degrees

• 30 degrees and 15 degrees

• 60 degrees and 45 degrees

• 90 degrees and 75 degrees

Why is the pair 60 degrees and 45 degrees chosen over 45 degrees and 30 degrees?

• It results in a simpler fraction

• It results in a larger angle

• It is easier to remember

• It is a more common pair

What is the tangent of 60 degrees?

• 1/2

• Square root 2

• Square root 3

• 1

What operation is used in the numerator of the tangent difference identity?

• Multiplication

• Division

• Addition

• Subtraction

What is the tangent of 45 degrees?

• Square root 3

• Square root 2

• 1

• 0

What is the result of rationalizing the denominator in the final expression?

• 1 - square root 3

• 1 + square root 3

• 2 - square root 3

• 2 + square root 3

What is the purpose of using the conjugate in the rationalization process?

• To eliminate the square root in the denominator

• To increase the value of the expression

• To change the sign of the expression

• To simplify the numerator

What is the final exact trigonometric value of tangent 15 degrees?

• 1 - square root 3

• 2 + square root 3

• 1 + square root 3

• 2 - square root 3