How to evaluate the half angle for cosine in radians

The video tutorial explains how to determine the cosine of an angle in different quadrants, emphasizing that cosine is negative in the second quadrant. It walks through the process of calculating the value of U, inserting it into an equation, and determining the sign based on quadrant analysis. The tutorial concludes with an example calculation, reinforcing the concept of cosine's behavior in various quadrants.

In which quadrant is the angle 7π/8 located, and what is the sign of cosine in that quadrant?

• Fourth quadrant, negative

• Third quadrant, positive

• Second quadrant, negative

• First quadrant, positive

What is the value of U if U/2 equals 7π/8?

• 7π/6

• 7π/4

• 7π/3

• 7π/2

When inserting U = 7π/4 into the equation, what is the resulting expression?

• sqrt(1 - cos(7π/4))/2

• -sqrt(1 - cos(7π/4))/2

• -sqrt(1 + cos(7π/4))/2

• sqrt(1 + cos(7π/4))/2

How does the quadrant of an angle affect the sign of the cosine value in the equation?

• The sign is always positive

• The sign is always negative

• The quadrant does not affect the sign

• The sign is determined by the quadrant

What is the simplified form of the expression involving square roots and cosine?

• 1/2 * sqrt(2)

• -1/2 * sqrt(2)

• -1/2 * sqrt(4)

• 1/2 * sqrt(4)