Sum and Difference Identities

Front

What is the sum identity for cosine?

Back

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

Front

What is the difference identity for cosine?

Back

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

Front

What is the sum identity for sine?

Back

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Front

What is the difference identity for sine?

Back

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Front

What is the tangent sum identity?

Back

tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))

Front

What is the tangent difference identity?

Back

tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))

Front

How can you express cos(175)cos(55) + sin(175)sin(55) using a cosine identity?

Back

It can be expressed as cos(175 - 55) = cos(120).

Front

What is the exact value of sin(-15°) using sum or difference identities?

Back

sin(-15°) = (√2 - √6) / 4.

Front

What is the exact value of cos(105°) using sum or difference identities?

Back

cos(105°) = (√2 - √6) / 4.

Front

What is the exact value of cos(75°) using sum or difference identities?

Back

cos(75°) = (√6 - √2) / 4.