Evaluate using the half angle formula for cosine

The video tutorial explains the cosine half angle formula and its application. It begins by introducing the formula and determining the quadrant for u/2, which affects the sign of the cosine value. The instructor then solves for u, calculates the cosine of pi over 4 using the unit circle, and simplifies the resulting fractions. The tutorial emphasizes understanding the trigonometric concepts and applying them to solve problems.

What determines whether the cosine of the half angle is positive or negative?

• The unit circle

• The value of pi

• The quadrant where u/2 lies

• The value of u

If u/2 equals pi/8, what is the value of u?

• pi/2

• pi/4

• pi/6

• pi/3

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

• 1

• 0

• Square root of 2 over 2

• Square root of 3 over 2

How can you simplify the expression with double fractions?

• Add 1 to both the numerator and denominator

• Multiply by 2 on the top and bottom

• Divide by 2 on the top and bottom

• Subtract 1 from both the numerator and denominator

What is the final simplified form of the expression?

• 2 plus the square root of 2 all over 2

• 2 plus the square root of 2 all over 4

• 2 minus the square root of 2 all over 4

• 2 minus the square root of 2 all over 2