Cosine Functions and Identities

This video tutorial covers the sum and difference identities for cosine, demonstrating how to use these identities to determine function values. It includes proofs of the identities and several example problems, such as finding the cosine of A plus B, cosine of 15 degrees, and cosine in radians. The video concludes with a problem involving cosine of 90 degrees, emphasizing the practical application of these identities.

What is the formula for the cosine of the sum of two angles?

• cos(A + B) = cos A * cos B + sin A * sin B

• cos(A + B) = cos A * cos B - sin A * sin B

• cos(A + B) = sin A * sin B - cos A * cos B

• cos(A + B) = sin A * cos B + cos A * sin B

In the proof of cosine identities, what is the significance of the reference angle?

• It determines the hypotenuse length.

• It is used to find the cosine values.

• It helps in finding the sine values.

• It is irrelevant to the proof.

How do you find the cosine of 15 degrees using sum or difference identities?

• By adding 45 and 60 degrees

• By subtracting 30 from 45 degrees

• By adding 30 and 45 degrees

• By subtracting 60 from 45 degrees

What is the exact value of cosine 15 degrees?

• (√3 - √2) / 4

• (√3 + √2) / 4

• (√6 - √2) / 4

• (√6 + √2) / 4

When converting radians to degrees, what is 7π/12 radians equivalent to?

• 135 degrees

• 120 degrees

• 105 degrees

• 90 degrees

Which angles in radians are used to find the cosine of 7π/12?

• π/3 and π/4

• π/4 and π/6

• π/2 and π/4

• π/3 and π/6

What is the result of cosine 7π/12 using the sum identity?

• (√2 + √6) / 4

• (√2 - √6) / 4

• (√3 + √6) / 4

• (√3 - √6) / 4

In the final example, what is the cosine of 90 degrees?

• -1

• Undefined

• 1

• 0

What identity is used when rewriting sine 40 degrees times cosine 50 degrees plus sine 40 degrees times sine 50 degrees?

• Sum identity

• Quotient identity

• Difference identity

• Product identity

What is the final result of the problem involving sine 40 degrees and cosine 50 degrees?

• 1

• -1

• Undefined

• 0