Solving an equations using the sum and difference formulas of cosine

The video tutorial explains how to use sum and difference formulas in trigonometry to solve equations. It covers the application of these formulas to cosine functions, demonstrating how to simplify and solve trigonometric equations. The tutorial also guides viewers through finding solutions on the unit circle, focusing on specific angles where the sine value equals negative square root of 2 over 2. The video emphasizes understanding the formulas and applying them to find solutions within a given range.

What is the formula for the cosine of the sum 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)sin(V) + cos(U)cos(V)

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

When applying the cosine difference formula, what is the expression for cos(X - π/4)?

• cos(X)cos(π/4) + sin(X)sin(π/4)

• cos(X)cos(π/4) - sin(X)sin(π/4)

• sin(X)sin(π/4) + cos(X)cos(π/4)

• sin(X)cos(π/4) - cos(X)sin(π/4)

What happens to the terms when you distribute the negative sign in the expression?

• The expression remains unchanged.

• Some terms cancel out.

• They all become negative.

• They all become positive.

What is the simplified form of the expression after distributing the negative sign?

• cos(X)cos(π/4) = 0

• 2 sin(X)sin(π/4) = -1

• sin(X)cos(π/4) = 0

• 2 sin(X)sin(π/4) = 1

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

• 1/2

• √3/2

• 1

• √2/2

Which angles have a sine value of -√2/2 between 0 and 2π?

• π and 2π

• π/2 and 3π/2

• 5π/4 and 7π/4

• π/4 and 3π/4

What is the process to rationalize the denominator of -1/√2?

• Subtract √2 from the denominator

• Add √2 to the numerator

• Multiply by √2/√2

• Divide by √2