Trigonometric Identities and Formulas

The video tutorial explains how to derive product-to-sum formulas for sines and cosines using angle sum identities. It covers the expansion of cosine angle sum identities, isolating cosine products, and deriving sine products by subtracting identities. The tutorial concludes with a discussion on the commutative property and its application in simplifying expressions.

What is the purpose of deriving product to sum formulas for sines and cosines?

• To combine multiple trigonometric functions into one

• To split expressions into a sum of two single trig functions

• To eliminate trigonometric functions from equations

• To simplify algebraic expressions

Which identity is used to expand cosine of a plus B?

• sine a sine B + cosine a cosine B

• sine a cosine B - cosine a sine B

• cosine a sine B + sine a cosine B

• cosine a cosine B - sine a sine B

What happens when you add the equations for cosine of a plus B and cosine of a minus B?

• The equations become zero

• The sine terms cancel out

• The cosine terms cancel out

• The equations become identical

How do you isolate cosine a cosine B from the sum of cosine of a plus B and cosine of a minus B?

• Subtract one

• Multiply by two

• Divide by two

• Add one

What is the first step in deriving the formula for sine a sine B?

• Divide the angle sum identities

• Add the angle sum identities

• Subtract the angle sum identities

• Multiply the angle sum identities

What is the result of subtracting the angle sum identities for sine a sine B?

• One sine a sine B

• Two cosine a cosine B

• Zero

• Two sine a sine B

How do you isolate sine a sine B after subtracting the angle sum identities?

• Multiply by two

• Divide by two

• Subtract one

• Add one

Which formula is used to derive sine a cosine B?

• Difference formula for sine

• Product to sum formula

• Angle sum formula for cosine

• Angle sum formula for sine

What happens when you add the equations for sine of a plus B and sine of a minus B?

• The equations become identical

• The cosine terms cancel out

• The equations become zero

• The sine terms cancel out

How do you isolate sine a cosine B after adding the angle sum identities?

• Add one

• Divide by two

• Subtract one

• Multiply by two