Pre-Calculus - Evaluating the cosine of an angle using the sum formula cos(11π/12)

The video tutorial explains how to evaluate the cosine of 11π/12 by expressing it as the sum of two angles, 3π/4 and π/6, which are found on the unit circle. The instructor demonstrates the use of the cosine addition formula, evaluates the cosine and sine of the individual angles, and simplifies the result. The importance of understanding the unit circle is emphasized for solving such problems.

What is the initial step in evaluating the cosine of 11π/12?

• Converting it to degrees

• Expressing it as the sum of two angles on the unit circle

• Using a calculator to find the value directly

• Using the sine function instead

Which formula is used to find the cosine of the sum of two angles?

• cos(A + B) = sin(A)sin(B) + cos(A)cos(B)

• cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

• cos(A + B) = cos(A)sin(B) + sin(A)cos(B)

• cos(A + B) = sin(A)cos(B) - cos(A)sin(B)

What is the cosine of 3π/4?

• -1/2

• 1/2

• -sqrt(2)/2

• sqrt(3)/2

What is the sine of π/6?

• sqrt(3)/2

• -sqrt(2)/2

• -1/2

• 1/2

Which of the following is a common coordinate point on the unit circle?

• sqrt(6)/2

• sqrt(7)/2

• sqrt(2)/2

• sqrt(5)/2

What is the result of multiplying and simplifying the terms for cosine of 11π/12?

• -sqrt(6) - sqrt(2) / 4

• sqrt(6) + sqrt(2) / 4

• -sqrt(3) - sqrt(2) / 2

• sqrt(3) + sqrt(2) / 2

What common factor can be factored out in the final expression?

• sqrt(3)/4

• sqrt(5)/4

• 1/4

• sqrt(2)/4