How to evaluate the half angle using the sine function

The video tutorial explains how to find the sine of π/8 using the half angle formula. It begins by introducing the problem and the half angle formula, then proceeds to solve for U by equating it to π/4. The cosine of π/4 is evaluated using the unit circle, and the expression is simplified to find the final solution for the sine of π/8.

What is the purpose of using the half angle formula in this problem?

• To calculate the tangent of π/8

• To determine the value of π

• To evaluate the cosine of π/4

• To find the exact value of sine of π/8

What is the value of U when U/2 is equal to π/8?

• π/4

• π/6

• π/3

• π/2

What is the cosine of π/4 according to the unit circle?

• 1

• √2/2

• √3/2

• 1/2

Why do we multiply the numerator and denominator by 2 in the simplification process?

• To eliminate the radical

• To make the expression more complex

• To keep the fraction equivalent

• To change the angle

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

• 1/2

• √2/2

• 1/2 times (2 - √2)

• 1/2 times (2 + √2)