Using the half angle of cosine to evaluate cos

The video tutorial covers the use of the half-angle formula to evaluate the cosine of angles that cannot be directly calculated using the unit circle. It explains the steps involved in applying the formula, highlights common mistakes students make, and demonstrates the evaluation of cosine for specific angles. The tutorial emphasizes the importance of understanding the formula and correctly applying it to avoid errors.

Why might the half-angle formula be preferred over sum or difference formulas for certain angles?

• It is the only method available.

• It avoids the need to find specific angle pairs.

• It is always more accurate.

• It is easier to remember.

What is the first step in using the half-angle formula for cosine?

• Find the sine of the angle.

• Determine the angle's quadrant.

• Set the angle equal to U/2.

• Use the sum formula.

When substituting into the half-angle formula, what common mistake should be avoided?

• Using the wrong trigonometric function.

• Using radians instead of degrees.

• Forgetting to square the result.

• Substituting the angle directly instead of U/2.

What is the cosine of 3π/4?

• -1/2

• 1/2

• -sqrt(2)/2

• sqrt(2)/2

How do you simplify the expression obtained from the half-angle formula?

• By adding the terms together.

• By applying the distributive property and simplifying the square root.

• By converting to degrees.

• By multiplying by 2.