Understanding Sine Sum and Difference Identities

This video tutorial covers the sum and difference identities for sine, explaining how to use these identities to determine function values. It includes a detailed explanation of the identities, followed by three example problems: calculating the sine of A - B with given values, finding the sine of 150 degrees using reference angles, and determining the sine of -π/12 using radians. The video concludes with a brief summary and encourages further exploration of the identities' proofs.

What is the formula for the sine of a sum of two angles?

• Sine A x Cosine B - Cosine A x Sine B

• Cosine A x Cosine B - Sine A x Sine B

• Sine A x Cosine B + Cosine A x Sine B

• Sine A x Sine B + Cosine A x Cosine B

How can the sum and difference identities for sine be combined?

• By multiplying the identities

• By adding the identities together

• By subtracting the identities

• By using a single formula with a +/- sign

In the first example, what is the value of sine A given in the problem?

• 4/5

• -5/13

• 3/5

• 5/13

What is the calculated value of sine A - B in the first example?

• 36/65

• -36/65

• 56/65

• -56/65

Which reference angles are used to find the sine of 150 degrees?

• 60 degrees and 45 degrees

• 60 degrees and 90 degrees

• 45 degrees and 60 degrees

• 30 degrees and 60 degrees

What is the exact value of sine 105 degrees found in the second example?

• Square root of 6 plus square root of 2 over 4

• Square root of 6 minus square root of 2 over 4

• Square root of 3 over 2

• Square root of 2 over 2

In the third example, what is the degree equivalent of -PI/12 radians?

• -15 degrees

• 15 degrees

• 30 degrees

• -30 degrees

What is the sine of PI/6 according to the unit circle?

• Square root of 3 over 2

• 1/2

• Square root of 2 over 2

• 1

What is the cosine of PI/4 according to the unit circle?

• 1/2

• Square root of 2 over 2

• 1

• Square root of 3 over 2

What is the final calculated value of sine -PI/12 in the third example?

• Square root of 2 minus square root of 6 over 4

• Square root of 2 plus square root of 6 over 4

• Square root of 6 minus square root of 2 over 4

• Square root of 6 plus square root of 2 over 4