Trigonometry Study Guide

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Trigonometry
sinθ =
opp
cosθ =
adj
tanθ =
Reciprocal identities
hyp
cscθ =
hyp
opp
hyp
secθ =
hyp
opp
cotθ =
adj
adj
sec θ =
cot θ =
s=rθ
Arc length
v=
Linear speed
rθ
t
ω=
Angular speed
Odd-Even func
Even
cos ( − θ)
Power reducing Formula
1
sinθ
1
cosθ
1
tan θ
Quotient identities
tanθ =
v =rω
sinθ
cosθ
cotθ =
t
cos(α + β ) = cos α cos β − sin α sin β
tan(−θ ) = − tanθ
cot(−θ ) = − cot θ
Pythagorean identities
2
2
sin θ + cos θ = 1
2
1 + tan θ = sec θ
1 + cot θ = csc θ
cos(α − β ) = cos α cos β + sin α sin β
tan(α + β ) =
a
b
=
1 − cos 2θ
1 + cos 2θ
sin
tan(α − β ) =
sinC
c
cos
tan
1 − tan α tan β
tan α − tan β
Double Angle Formula
sin 2θ = 2 sinθ cosθ
2
2
2
To be used when SAS
2
θ
2
θ
2
=±
1 − cosθ
2
=±
1 + cosθ
2
=±
1 − cosθ
1 + cosθ
=
1 − cosθ
sinθ
=
sinθ
1 + cosθ
2
2
cos 2θ = cos θ − sin θ
Graphing trig func
normal
y = ± A sin(Bx − C ) + D
2
= 2 cos θ − 1
tan 2θ =
2 tanθ
1 − tan2 θ
Flips
A = amplitude
y
− y min
= max
2
B=
Law of cosines
a = b + c − 2bc cos A
θ
1 + tan α tan β
2
sin B
tan2 θ =
tan α + tan β
= 1 − 2 sin θ
Law of sines
=
1 + cos 2θ
2
Sum & Difference
sec ( − θ) = sec θ
csc ( − θ) = − csc θ
sin A
sinθ
sin(α − β ) = sin α cos β − cos α sin β
2
cos2 θ =
cosθ
= cosθ
2
1 − cos 2θ
2
Half-Angle Formula
sin(α + β ) = sin α cos β + cos α sin β
2
sin2 θ =
θ
sin ( − θ
θ)) = − sinθ
Odd
csc θ =
adj
opp
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2π
period
Period =
2π
B
phase shift =
if
C
B
C
B
> 0, shift to right
D = vertical shift