TRIGONOMETRY REFERENCE SHEET
Right Triangle Definitions
opp
adj
=
sin θ
=
cos θ
hyp
hyp
opp
adj
=
tan θ
=
cotθ
adj
opp
hyp
hyp
=
sec θ
=
csc θ
adj
opp
Circular Definitions
y
=
cos θ
r
y
=
tan θ
=
cotθ
x
r
=
sec θ
=
csc θ
x
=
sin θ
x
r
x
y
r
Pythagorean Identities
− sin(θ ) cos( −θ ) =
sin( −θ ) =
cos(θ )
− tan(θ ) cot( −θ ) =
− cot(θ )
tan( −θ ) =
− csc(θ )
sec( −θ ) =
sec(θ )
csc( −θ ) =
sin θ + cos θ =
1
2
2
2
2
2
1 + tan θ =
sec θ
1 + cot θ =
csc θ
sin θ
cos θ
=
cot θ
cos θ
sin θ
1
1
=
=
sec θ
csc θ
cos θ
sin θ
=
tan θ
y
Even/Odd Properties
2
Other Identities
Double Angle Identities
sin(2θ ) = 2 sin θ cos θ
cos(2
=
θ)
2
2
cos θ − sin θ
2
2 cos θ − 1
2
1 − 2 sin θ
Special Angles
π
cos 0 1=
cos
=
6
3
π
cos
=
2
4
π 1
π
sin 0 0=
sin
sin
=
=
6 2
4
π 1
π
cos
cos
0
=
=
2
3 2
2
2
π
3
π
sin
sin
1
=
=
2
3
2
2
2
Sum and Difference Formulas
Power Reducing Formulas
2
1 − cos(2u )
2
2
1 + cos(2u )
sin u =
cos(u ± v )= cos u ⋅ cos v  sin u ⋅ sin v
sin(u ± v )= sin u ⋅ cos v ± cos u ⋅ sin v
cos u =
2
Cofunction Identities
π

π

sin=
 − x  cos x tan=
 − x  cot x
2
2




π

sec  − x  =
csc x
2 