Trigonometric Functions and Angles

The video tutorial explains how to solve for the cosine of 160 degrees using the unit circle and sum and difference formulas. It begins by discussing the difficulty of finding the cosine of 160 directly on the unit circle and proceeds to break down the problem using known angles and formulas. The instructor demonstrates the calculation of cosine for 120 and 45 degrees, and then applies these to find the cosine of 165 degrees. The tutorial concludes with a simplification of the final answer.

What is the cosine of 60 degrees on the unit circle?

• -1/2

• 0

• √3/2

• 1/2

Why is it difficult to find the cosine of 160 degrees directly on the unit circle?

• It is greater than 180 degrees.

• It is less than 90 degrees.

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

• It is a negative angle.

Which angles are typically used to find exact trigonometric values?

• 30, 45, 60, 90

• 15, 75, 105, 135

• 0, 180, 270, 360

• 10, 20, 30, 40

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

• cos(u + v) = cos(u)sin(v) - sin(u)cos(v)

• cos(u + v) = sin(u)cos(v) + cos(u)sin(v)

• cos(u + v) = sin(u)sin(v) + cos(u)cos(v)

• cos(u + v) = cos(u)cos(v) - sin(u)sin(v)

What is the cosine of 120 degrees?

• -√3/2

• √3/2

• 1/2

• -1/2

What is the cosine of 45 degrees?

• √2/2

• 1/2

• √3/2

• -1/2

What mistake was corrected regarding the angle calculation?

• Incorrectly calculating sine

• Using the wrong formula

• Misplacing the decimal point

• Misidentifying the angle as 150 degrees

What is the final simplified expression for the cosine of 165 degrees?

• (√3 - √2)/4

• -(√2 + √6)/4

• (√2 - √6)/4

• -(√3 + √2)/4