Solving an equations using the sum and difference formulas of cosine

The video tutorial explains the use of trigonometric sum and difference formulas to solve equations. It begins with an introduction to the formulas for cosine, followed by their application to specific angles. The tutorial then demonstrates how to simplify expressions and solve equations using these formulas. Finally, it guides viewers through finding solutions within a specified range using the unit circle.

What is the sum formula for cosine of two angles?

• cos(U + V) = cos(U)cos(V) - sin(U)sin(V)

• cos(U + V) = cos(U)cos(V) + sin(U)sin(V)

• cos(U + V) = sin(U)cos(V) - cos(U)sin(V)

• cos(U + V) = sin(U)sin(V) + cos(U)cos(V)

When applying the cosine difference formula, what is the expression for cos(U - V)?

• cos(U - V) = cos(U)cos(V) - sin(U)sin(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 happens to the expression when you distribute the negative sign in the parentheses?

• The terms become positive.

• The terms remain unchanged.

• The terms become negative.

• The terms cancel each other out.

How do you simplify the expression 2 * sin(X) * sin(π/4) = -1?

• Divide by 2 and sin(π/4)

• Divide by sin(π/4) and multiply by 2

• Multiply by 2 and divide by sin(π/4)

• Divide by 2 and multiply by sin(π/4)

What is the sine value of π/4 on the unit circle?

• 1/2

• sqrt(2)/2

• sqrt(3)/2

• 1

Which angles have a sine value of -sqrt(2)/2 within the interval [0, 2π]?

• π/4 and 3π/4

• π/2 and 3π/2

• π and 2π

• 5π/4 and 7π/4

What is the process to rationalize the denominator of -1/sqrt(2)?

• Add sqrt(2)

• Divide by sqrt(2)

• Multiply by sqrt(2)/sqrt(2)

• Subtract sqrt(2)