Evaluate the half angle in radians for cosine

The video tutorial explains how to determine the sign of cosine based on the angle's position in different quadrants. It covers the application of the cosine formula, emphasizing the importance of recognizing when cosine is negative. The tutorial also discusses handling fractions in calculations and the significance of angle positions in determining the sign of trigonometric functions.

In which quadrant does the angle 5π/8 lie, and what is the sign of cosine in that quadrant?

• Second quadrant, negative

• Fourth quadrant, negative

• First quadrant, positive

• Third quadrant, positive

What is the cosine of 5π/4, and in which quadrant does this angle lie?

• -√2/2, third quadrant

• √2/2, fourth quadrant

• √2/2, first quadrant

• -√2/2, second quadrant

When adjusting the cosine formula for an angle in the third quadrant, what should be considered?

• The formula should be positive

• The angle should be converted to degrees

• The angle should be doubled

• The formula should be negative

Why is it important to be cautious with angles expressed in uncommon fractions like eighths or twelfths?

• They are always negative

• They simplify calculations

• They can lead to incorrect quadrant identification

• They are always positive

What is the general rule for determining the sign of cosine based on the quadrant?

• Cosine is positive in the second and fourth quadrants

• Cosine is negative in the second and third quadrants

• Cosine is negative in the first and third quadrants

• Cosine is always positive