1. Maths 3/4: Trigonometry - Formulas & Identities
1. Trigonometric Functions of Acute Angles
sin X = a / c
csc X = c / a Basic
tan X = a / b
cot X = b / a
cos X = b / c
sec X = c / b
2. Special Triangles
Special triangles may be used to find trigonometric functions of special
angles: 30, 45 and 60 degress.
3. Sine and Cosine Laws in Triangles
3.1 - The sine law
sin A/a = sin B/b = sin C/c
3.2 - The cosine laws
2. a 2 = b 2 + c 2 - 2bc cos A
b 2 = a 2 + c 2 - 2ac cos B
c 2 = a 2 + b 2 - 2ab cos C
4. Relations Between Trigonometric Functions
cscX = 1 / sinX, sinX = 1 / cscX
secX = 1 / cosX, cosX = 1 / secX
tanX = 1 / cotX, cotX = 1 / tanX
tanX = sinX / cosX, cotX = cosX / sinX
5. Pythagorean Identities
sin 2X + cos 2X = 1
1 + tan 2X = sec 2X
1 + cot 2X = csc 2X
6. Negative Angle Identities
sin(-X) = - sinX , odd function
csc(-X) = - cscX , odd function
cos(-X) = cosX , even function
sec(-X) = secX , even function
tan(-X) = - tanX , odd function
cot(-X) = - cotX , odd function
7. Cofunctions Identities
sin(pi/2 - X) = cosX
cos(pi/2 - X) = sinX
tan(pi/2 - X) = cotX