Pre-Calculus - Use The Double Angle Formula for Tangent to Evaluate for an Angle

The video tutorial explains the properties of angle U, which lies between π/2 and π, placing it in the second quadrant. It covers the cosine of angle U, emphasizing the relationship between adjacent and hypotenuse sides. The tutorial then focuses on solving for the tangent of 2U, using the Pythagorean theorem to find the opposite side. Finally, it demonstrates the algebraic process to calculate the tangent of 2U, resulting in a final answer of 4√5.

In which quadrant does angle U lie if it is greater than π/2 but less than π?

• First quadrant

• Third quadrant

• Fourth quadrant

• Second quadrant

What is the cosine of angle U if the adjacent side is -2 and the hypotenuse is 3?

• -3/2

• 2/3

• 3/2

• -2/3

Which theorem is used to find the opposite side of the triangle when solving for tangent of 2U?

• Cosine Rule

• Sine Rule

• Pythagorean Theorem

• Law of Tangents

What is the formula for the tangent of 2U?

• 2 * tangent(U) / (1 - tangent^2(U))

• tangent(U) / (1 + tangent^2(U))

• 2 * tangent(U) / (1 + tangent^2(U))

• tangent(U) / (1 - tangent^2(U))

What is the final answer for the tangent of 2U after completing the algebraic manipulation?

• 2 sqrt(5)

• 3 sqrt(5)

• 5 sqrt(5)

• 4 sqrt(5)