Sum and Difference Identities

Front

What is the sum identity for sine?

Back

sin(α + β) = sin(α)cos(β) + cos(α)sin(β)

Front

What is the difference identity for sine?

Back

sin(α - β) = sin(α)cos(β) - cos(α)sin(β)

Front

What is the sum identity for cosine?

Back

cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

Front

What is the difference identity for cosine?

Back

cos(α - β) = cos(α)cos(β) + sin(α)sin(β)

Front

What is the tangent sum identity?

Back

tan(α + β) = (tan(α) + tan(β)) / (1 - tan(α)tan(β))

Front

What is the tangent difference identity?

Back

tan(α - β) = (tan(α) - tan(β)) / (1 + tan(α)tan(β))

Front

Calculate sin(105º) using the sum identity.

Back

sin(105º) = sin(60º + 45º) = sin(60º)cos(45º) + cos(60º)sin(45º) = (√3/2)(√2/2) + (1/2)(√2/2) = 1/4(√2 + √6)

Front

Calculate cos(175)cos(55) + sin(175)sin(55) using the cosine sum identity.

Back

cos(175 - 55) = cos(120)

Front

Find the exact value of cos(20)cos(40) - sin(20)sin(40).

Back

Using the cosine difference identity: cos(20 + 40) = cos(60) = 1/2.

Front

Which angles are solutions to sin θ = √(3)/2?

Back

The solutions are θ = π/3 and θ = 2π/3.