How to evaluate the half angle of tangent in radians

The video tutorial explains the application of tangent functions, focusing on two forms involving cosine and sine. It emphasizes using the half angle formula for tangent, particularly when the half angle is π/8, leading to simplification of complex fractions. The tutorial further demonstrates rationalizing denominators and applying the distributive property, highlighting common arithmetic challenges in precalculus.

Which form of the tangent function does the instructor recommend using?

• 1 minus cosine of Theta divided by sine of Theta

• Sine of Theta divided by 1 minus cosine of Theta

• Sine of Theta divided by 1 plus cosine of Theta

• 1 plus cosine of Theta divided by sine of Theta

What is the value of Theta when the half angle is π/8?

• π/4

• π/2

• π/3

• π/6

What is the first step in simplifying the complex fraction involving square roots?

• Divide the denominators

• Multiply by the reciprocal

• Add the fractions

• Subtract the numerators

After rationalizing the denominator, what is the simplified expression?

• sqrt 2 + 1

• 2 + sqrt 2

• 2 - sqrt 2

• sqrt 2 - 1

What is the main challenge in solving the problem according to the instructor?

• Understanding precalculus concepts

• Performing arithmetic operations

• Memorizing formulas

• Applying calculus techniques