Understanding Tangent of 13π/12

The video tutorial explains how to compute the tangent of 13π/12 without a calculator. It begins by breaking down the angle into a sum of two angles, 5π/4 and -π/6, and uses the tangent sum formula. The video then demonstrates how to find the tangent of each angle using the unit circle and properties of special triangles. Finally, it combines these results to find the tangent of 13π/12.

What is the first step in finding the tangent of 13π/12 without a calculator?

• Directly use the tangent addition formula.

• Express 13π/12 in terms of angles with known tangents.

• Approximate the value using a graph.

• Use a calculator to find the exact value.

Which formula is used to find the tangent of the sum of two angles?

• Sine addition formula

• Cosine addition formula

• Tangent addition formula

• Pythagorean theorem

What is the tangent of 5π/4?

• Undefined

• 0

• 1

• -1

Which type of triangle is used to find the tangent of 5π/4?

• Scalene triangle

• Equilateral triangle

• 45-45-90 triangle

• 30-60-90 triangle

What is the tangent of -π/6?

• -√3

• √3

• -1/√3

• 1/√3

Which type of triangle is used to find the tangent of -π/6?

• Equilateral triangle

• 30-60-90 triangle

• Scalene triangle

• 45-45-90 triangle

What is the final expression for the tangent of 13π/12?

• (√3 - 1)/(√3 + 1)

• √3 - 1

• √3 + 1

• (√3 + 1)/(√3 - 1)

What operation is performed to simplify the expression for tangent of 13π/12?

• Multiplication by √3

• Subtraction

• Division by √3

• Addition

What is the significance of the unit circle in this problem?

• It provides exact values for cosine.

• It helps in visualizing angles and their tangents.

• It is used to calculate sine values.

• It is irrelevant to the problem.

Why is it important to express angles in terms of known angles?

• To make calculations easier without a calculator.

• To avoid using trigonometric identities.

• To directly find the sine value.

• To simplify the cosine calculation.