Half angle of Cosine given an angle in radians

The video tutorial explains the concept of half angle identities, focusing on calculating angles from half angles and applying the cosine formula. It emphasizes the importance of determining the correct sign based on the quadrant and simplifies the cosine expression. The tutorial also clarifies the half angle formula, ensuring a comprehensive understanding of the topic.

What is the first step in solving a problem using half angle identities?

• Multiply the half angle by 2 to find the full angle

• Use the sine formula

• Convert the angle to degrees

• Divide the angle by 2

In which quadrant is pi over 12 located, and what does this imply for the cosine value?

• Second quadrant, negative cosine

• Third quadrant, negative cosine

• First quadrant, positive cosine

• Fourth quadrant, positive cosine

How do you calculate the cosine of pi over 12 using the half angle formula?

• 1 minus the cosine of pi over 6 divided by 2

• 1 plus the sine of pi over 6 divided by 2

• 1 plus the cosine of pi over 6 divided by 2

• 1 minus the sine of pi over 6 divided by 2

What is the cosine of pi over 6?

• 3/2

• Square root of 2 over 2

• Square root of 3 over 2

• 1/2

Why is it important to use the full angle in the half angle formula?

• The half angle is not used in trigonometry

• The full angle is easier to calculate

• The half angle is always negative

• The formula requires the full angle for accurate results