Pre-Calculus - How to solve using the addition formula of two angles for cosine cos(160)

The video tutorial explains how to calculate the cosine of 165 degrees using the unit circle and sum and difference formulas. It begins with a review of the unit circle and the difficulty of finding the cosine of 160 degrees directly. The instructor then corrects the problem to 165 degrees and demonstrates how to use the sum and difference formulas to find the exact value. The process involves identifying angles that add up to 165 degrees, applying the formulas, and simplifying the result to reach the final answer.

What is the main challenge in finding the cosine of 160 degrees using the unit circle?

• It is greater than 180 degrees.

• It is a negative angle.

• It requires a calculator for exact values.

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

Which two angles are used to express 165 degrees in the sum and difference formulas?

• 60 and 105 degrees

• 120 and 45 degrees

• 90 and 75 degrees

• 150 and 15 degrees

What is the cosine of 120 degrees?

• -√3/2

• 1/2

• -1/2

• √3/2

What is the sine of 45 degrees?

• 1/2

• √2/2

• -1/2

• √3/2

What is the result of multiplying the cosine of 120 degrees by the cosine of 45 degrees?

• -√3/4

• -√2/4

• √3/4

• √2/4

What is the simplified form of the expression obtained from the sum and difference formulas?

• -1/2 - √3/2

• -√2/4 - √6/4

• √2/4 + √6/4

• -√2/4 + √6/4

What can be factored out from the final expression to simplify it further?

• √2

• 1/4

• 1/2

• √3