Using sum of two angles to evaluate an angle in radians for tangent, tan

The video tutorial explains how to solve a tangent problem using the tangent formula. It covers the importance of understanding the unit circle, plugging in values, simplifying fractions, and rationalizing the denominator. The tutorial emphasizes the need to avoid mistakes by carefully following each step, ultimately leading to the final solution of the problem.

What is the main challenge in evaluating the tangent of 11π/12 directly?

• It is a negative angle.

• It is not a standard angle on the unit circle.

• It is an angle greater than 2π.

• It is an angle less than 0.

Which formula is used to evaluate the tangent of a sum of angles?

• tan(U + V) = tan U + tan V

• tan(U + V) = (tan U + tan V) / (1 - tan U tan V)

• tan(U + V) = tan U * tan V

• tan(U + V) = (tan U - tan V) / (1 + tan U tan V)

What is the tangent of π/6?

• 0

• 1

• sqrt(3)/3

• sqrt(3)

How is the tangent of 3π/4 calculated using the unit circle?

• By using the identity tan(3π/4) = tan(π/4).

• By reflecting the point of π/4 over the x-axis.

• By reflecting the point of π/4 over the y-axis.

• By using the identity tan(3π/4) = -tan(π/4).

What is the result of multiplying by the conjugate in the simplification process?

• It eliminates the imaginary part.

• It simplifies the expression to a single fraction.

• It rationalizes the denominator.

• It changes the sign of the numerator.

What is the final simplified form of the expression for tan(11π/12)?

• -2 + sqrt(3)

• sqrt(3) - 2

• 2 - sqrt(3)

• -sqrt(3) + 2

Why is it important to multiply by the conjugate during simplification?

• To rationalize the denominator.

• To simplify the numerator.

• To increase the value of the expression.

• To eliminate complex numbers.