Pythagorean Identities Power Reducing Formulas Double

1 Page of Trigonometry Formulas by www.ReeTutorsMath.org
Pythagorean Identities
Sum and Difference Formulas
sin(A + B)
=
sin(A) cos(B) + cos(A) sin(B)
sin2 (θ) + cos2 (θ)
=
1
sin(A − B)
=
sin(A) cos(B) − cos(A) sin(B)
tan2 (θ) + 1
=
sec2 (θ)
cos(A + B)
=
cos(A) cos(B) − sin(A) sin(B)
1 + cot2 (θ)
=
csc2 (θ)
cos(A − B)
=
cos(A) cos(B) + sin(A) sin(B)
tan(A + B)
=
tan(A) + tan(B)
1 − tan(A) tan(B)
tan(A − B)
=
tan(A) − tan(B)
1 + tan(A) tan(B)
Power Reducing Formulas
2
sin (θ)
=
cos2 (θ)
=
tan2 (θ)
=
1 − cos(2θ)
2
1 + cos(2θ)
2
1 − cos(2θ)
1 + cos(2θ)
Double-Angle Formulas
sin(2θ)
=
2 sin(θ) cos(θ)
cos(2θ)
=
cos2 (θ) − sin2 (θ)
cos(2θ)
=
2 cos2 (θ) − 1
cos(2θ)
=
1 − 2 sin2 (θ)
=
2 tan(θ)
1 − tan2 (θ)
tan(2θ)
Product-to-Sum Formulas
sin(A) sin(B)
=
1
[cos(A − B) − cos(A + B)]
2
cos(A) cos(B)
=
1
[cos(A − B) + cos(A + B)]
2
sin(A) cos(B)
=
1
[sin(A − B) + sin(A + B)]
2
Sum-to-Product Formulas
sin(A) + sin(B)
=
2 sin
sin(A) − sin(B)
=
cos(A) + cos(B)
=
Half-Angle Formulas
θ
sin
2
θ
cos
2
θ
tan
2
θ
tan
2
r
=
+
−
r
1 − cos(θ)
2
cos(A) − cos(B)
+
−
=
1 − cos(θ)
sin(θ)
=
sin(θ)
1 + cos(θ)
www.ReeTutorsMath.org/notes
A+B
2
A−B
2
A−B
2
cos
sin
A−B
A+B
cos
2
2
A+B
A−B
= −2 sin
sin
2
2
1 + cos(θ)
2
=
2 cos
A+B
2
2 cos