Given Sine, evaluate the half angle of cosine

The video tutorial explains how to find the exact values of cosine using the half angle formulas. It begins by setting up the problem with a given sine value and constraints. The instructor then uses the Pythagorean theorem to find the cosine value, considering the angle's position in the second quadrant. The half angle formula for cosine is applied, and the expression is simplified by rationalizing the denominator, resulting in the final solution.

What is the given sine value in the problem?

• 13/5

• 5/13

• 12/13

• 5/12

Which theorem is used to find the cosine value?

• Tangent Rule

• Sine Rule

• Cosine Rule

• Pythagorean Theorem

In which quadrant is the angle located?

• Fourth Quadrant

• Third Quadrant

• Second Quadrant

• First Quadrant

What is the half-angle formula for cosine?

• cos(U/2) = ± sqrt(1 + sin U) / 2

• cos(U/2) = ± sqrt(1 + cos U) / 2

• cos(U/2) = ± sqrt(1 - sin U) / 2

• cos(U/2) = ± sqrt(1 - cos U) / 2

What is the final simplified result of the half-angle formula for cosine?

• ± sqrt(26) / 13

• ± sqrt(13) / 26

• ± sqrt(26) / 26

• ± sqrt(13) / 13