Sum & Difference Formulas
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Transcript of Sum & Difference Formulas
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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°
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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
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Using Sum/Diff to Find Exact Values
Find the sine for 285°, using the fact 285°=330° – 45°
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Using Sum/Diff to Find Exact Values
Find the cosine for 5
12
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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.
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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
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Using Sum/Diff to Verify
Verify the identity
sin(x + y)sin(x – y) = sin2x – sin2y
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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