Using sum and difference formula to find the exact value with cosine

The video tutorial covers the challenge of finding angles on the unit circle, specifically π/12 and 7π/12. It explains how to break these angles into sums or differences of known angles like π/3 and π/4. The tutorial compares working with degrees and radians, highlighting the ease of degrees. It also demonstrates using the cosine addition formula to solve trigonometric problems, emphasizing the importance of identifying angles and using the unit circle for validation.

Why is it challenging to find the angle for π/12 on the unit circle?

• Because π/12 is an imaginary number.

• Because π/12 is a negative angle.

• Because π/12 is greater than π.

• Because π/12 is not a standard angle on the unit circle.

What is the purpose of finding common denominators when breaking down angles?

• To convert angles into degrees.

• To ensure angles can be added or subtracted correctly.

• To simplify the angles into smaller fractions.

• To find the exact value of the angle.

Which of the following is a correct breakdown of 7π/12 using known angles?

• π/2 + π/6

• π/4 + π/4

• π/3 + π/4

• π/6 + π/6

What is the first step in applying the cosine addition formula?

• Convert angles to degrees.

• Subtract the angles.

• Identify the angles U and V.

• Multiply the angles together.

What is the result of simplifying the expression for the cosine of π/3 plus π/4?

• 1/2 - sqrt 2 / 2

• sqrt 2 / 4 - sqrt 6 / 4

• 1/2 + sqrt 3 / 2

• sqrt 3 / 4 + sqrt 2 / 4