Using the additions of two angles and cosine

The video tutorial explains how to find the exact value of cosine for 13π/12 using the unit circle and the sum formula for cosine. The instructor breaks down the angle into the sum of two angles on the unit circle, applies the sum formula, and calculates the exact values using known coordinates. The process involves identifying the correct angles, applying trigonometric identities, and simplifying the result to find the cosine of 13π/12.

Why can't the exact value of cosine for 13π/12 be directly calculated using the unit circle?

• The angle is not a standard angle on the unit circle.

• The unit circle only works for angles in degrees.

• Cosine values are only available for angles less than π.

• The unit circle does not support angles greater than 2π.

Which two angles are used to break down 13π/12 for cosine calculation?

• π/2 and π/4

• 3π/4 and π/3

• π/6 and π/3

• π/4 and π/6

What is the cosine sum formula used in this context?

• cos(U + V) = sin(U) * cos(V) - cos(U) * sin(V)

• cos(U + V) = cos(U) * cos(V) + sin(U) * sin(V)

• cos(U + V) = cos(U) * cos(V) - sin(U) * sin(V)

• cos(U + V) = cos(U) + cos(V)

What are the cosine and sine values for the angle 3π/4?

• cos: -√2/2, sin: √2/2

• cos: √3/2, sin: 1/2

• cos: 1/2, sin: √3/2

• cos: -1/2, sin: -√3/2

What is the final result for the cosine of 13π/12 after calculation?

• -√3/2

• -1

• -1/2

• -√2/4