Download Math 1275/D500 Instructor: Suman Ganguli Fundamental

Math 1275/D500
Instructor: Suman Ganguli
Fundamental Trigonometric Identities
tan θ =
sin θ
cos θ
cot θ =
1
cos θ
=
tan θ
sin θ
csc θ =
1
sin θ
sec θ =
1
cos θ
sin2 θ + cos2 θ = 1 =⇒ sin2 θ = 1 − cos2 θ& cos2 θ = 1 − sin2 θ
tan2 θ + 1 = sec2 θ
cot2 θ + 1 = csc2 θ
Law of Sines & Law of Cosines
For any triangle (i.e., not necessarily a right triangle) with sidelengths a, b, c and corresponding
angles A, B, C (as shown):
Law of Sines:
sin A
a
=
sin B
sin C
=
b
c
Law of Cosines:
a2
=
b2 + c2 − 2bc cos A
b2
=
a2 + c2 − 2ac cos B
2
=
a2 + b2 − 2ab cos C
c