Learn how to evaluate for the tangent of an angle using half angles

The video tutorial explains how to evaluate the tangent of 3π/8 using trigonometric identities. It begins by setting up the problem using the half-angle identity and solving for U. The instructor then simplifies the tangent expression by eliminating fractions and using the conjugate to achieve a final simplified form. The tutorial emphasizes common mistakes students make and provides step-by-step guidance to avoid them.

What is the first step in evaluating the tangent of 3π/8 using the half-angle identity?

• Multiply both sides by 3

• Set U/2 equal to 3π/8

• Add π to both sides

• Divide by 4

When using the unit circle, what is the sine value for 3π/4?

• 1

• -√2/2

• √2/2

• 0

What common mistake do students make when substituting values in this problem?

• Using the wrong angle

• Forgetting to multiply by 2

• Dividing by π

• Plugging in 3π/4 for U

What mathematical technique is used to eliminate the term in the denominator?

• Adding fractions

• Subtracting squares

• Using the conjugate

• Multiplying by zero

What is the final simplified expression for the tangent of 3π/8?

• 4 - 2

• √2 / (2 - √2)

• 3π/4

• 2 + 2√2