Sum & Difference FormulasObjective: Be able to use sum & difference formulas to find trig functions of non-unit circle values, simplify, verify, solve, etc, etc.

TS: Explicitly assess information and draw conclusions

Warm-Up: Find the exact value of each.

a) sin(390°+120°)

b) sin390° + sin120°

Sum and Difference Formulas

sin( ) sin cos cos sinu v u v u v sin( ) sin cos cos sinu v u v u v

cos( ) cos cos sin sinu v u v u v cos( ) cos cos sin sinu v u v u v

tan tantan( )

1 tan tan

u vu v

u v

tan tan

tan( )1 tan tan

u vu v

u v

Using Sum/Diff to Find Exact Values

Find the sine for 285°, using the fact 285°=330° – 45°

Using Sum/Diff to Find Exact Values

Find the cosine for 5

12

Using Sum/Diff to Find Exact Values

Find tan(u+v) where sin(u) = -7/25 & cos(v) = -4/5. Both u & v are in quadrant III.

Using Sum/Diff to SimplifyWrite the expression as the sine, cosine or tangent

of an angle.

a) cos(0.88)cos(0.34)+sin(0.88)sin(0.34)

b)4 4

sin cos cos sin9 8 9 8

Using Sum/Diff to Verify

Verify the identity

sin(x + y)sin(x – y) = sin2x – sin2y

5: ,6 6

5 7: ,

4 4

Ans

Ans

You Try!Verify each identity1) sin(3π - x) = sinx2) cos(x + y) + cos(x - y) = 2cosxcosy3)

Solve for x in the interval [0, 2π)4)

5)

sin( )tan tan

cos cos

2sin 3tan 02

x x

cos( ) cos( ) 14 4

x x