Solving an equation using the sum and difference formulas for cosine

The video tutorial explains the cosine sum and difference formulas, demonstrating how to apply them by substituting values and simplifying expressions. It emphasizes the importance of using parentheses to avoid errors and shows how to evaluate trigonometric functions using the unit circle. The tutorial concludes with solving trigonometric equations to find specific angle values within a given range.

What is the formula for the cosine of the sum of two angles U and V?

• sin(U) * cos(V) + cos(U) * sin(V)

• cos(U) * cos(V) - sin(U) * sin(V)

• sin(U) * sin(V) - cos(U) * cos(V)

• cos(U) * cos(V) + sin(U) * sin(V)

When applying the cosine difference formula, why is it important to use parentheses?

• To ensure the correct order of operations

• To avoid forgetting to distribute the negative sign

• To make the expression look neat

• To simplify the calculation

What is the value of sine of π/4?

• 1/2

• √2/2

• 0

• 1

How do you simplify the expression -2 * sin(X) * √2/2?

• -sin(X)

• 2 * sin(X)

• √2 * sin(X)

• -√2 * sin(X)

What is the final simplified form of sine of X in the given problem?

• -√2/2

• 1/√2

• -1/2

• √2/2

In which quadrants is the sine of an angle negative?

• First and second

• Second and third

• First and fourth

• Third and fourth

What are the angles where sine of X equals -√2/2 between 0 and 2π?

• π and 2π

• 5π/4 and 7π/4

• π/2 and 3π/2

• π/4 and 3π/4