Download Trigonometric Formulas

Trigonometric Formulas
Right Angle Trigonometry
opp
hyp
sin θ =
cscθ =
hyp
opp
hyp
adj
hyp
cos θ =
secθ =
θ
hyp
adj
adj
opp
adj
tan θ =
cot θ =
adj
opp
opp
Trigonometric functions on the Unit circle
1
y
cscθ =
sin θ = y
y
(x,y)
cos θ = x
tan θ =
Fundamental Identities
1
1
sin θ =
cos θ =
cscθ
secθ
1
1
cscθ =
secθ =
sin θ
cos θ
y
x
1
x
x
cot θ =
y
θ
secθ =
sin θ
cos θ
cos θ
cot θ =
sin θ
1
cot θ
1
cot θ =
tan θ
tan θ =
tan θ =
Pythagorean Identities
cos 2 θ + sin 2 θ = 1
1 + tan 2 θ = sec 2 θ
cot 2 θ + 1 = csc2 θ
Negative Angle Identities
sin(−θ ) = − sin θ
cos ( −θ ) = cos θ
tan ( −θ ) = − tan θ
Sum and Difference Formulas
sin( A ± B) = sin A cos B ± cos A sin B
cos( A ± B ) = cos A cos B ∓ sin A sin B
tan A ± tan B
tan( A ± B) =
1 ∓ tan A tan B
Cofunction Identities
sin( π2 − θ ) = cos θ
tan( π2 − θ ) = cot θ
sec( π2 − θ ) = cscθ
Double-Angle Formulas
sin(2θ ) = 2 sin θ cosθ
Half-Angle Formulas
1 − cos 2θ
sin 2 θ =
2
1 + cos 2θ
cos 2 θ =
2
1 − cos 2θ
tan 2 θ =
1 + cos 2θ
cos(2θ ) = cos 2 θ − sin 2 θ
= 2 cos 2 θ − 1
= 1 − 2sin 2 θ
2 tan θ
tan(2θ ) =
1 − tan 2 θ
Product-to-Sum Formulas
sin A cos B = 12 [sin( A + B) + sin( A − B )]
[sin( A + B) − sin( A − B)]
cos A cos B = 12 [cos( A − B ) + cos( A + B )]
sin A sin B = 12 [cos( A − B) − cos( A + B )]
cos A sin B =
1
2
x
cos( π2 − θ ) = sin θ
cot( π2 − θ ) = tan θ
csc( π2 − θ ) = secθ
B
Law of Sines
sin A sin B sin C
=
=
a
b
c
Law of Cosines
c 2 = a 2 + b 2 − 2ab cos C
a
c
A
b
C