Trigonometry

Definition: Trigonometry is the study of the Ratio relationships

between the sides and angles of a Right Triangle.

B

Hypotenuse = c

Opposite = a

A

C

Adjacent = b

Angles: A, B, C Sides: a,b,c

Relationships of Angle A to Sides: Opposite, Adjacent, and Hypotenuse sides.

Relationships for Angle B can be defined by analogous ratios.

SOH! CAH! TOA!

Sin A = O/H Cos A = A/H Tan A = O/A

Csc A = H/O Sec A = H/A Cot A = A/O

Csc A = 1/Sin Sec A = 1/Cos Cot A = 1/Tan

There are two other important relationships for a Right Triangle.

The Sum of the Angles of any Triangle equals 180 Degrees.

Euclidean Theorem: <A + <B + <C = 180⁰

The Sum of the Squares of Sides equals the Square of the Hypotenuse!

Pythagorean Theorem: a² + b² = c²

^{************************************************************************}

Trigonometric ( Sin Cos Tan ) Relationships

Hypotenuse Opposite Adjacent

O
		A	A	A	A

Sin Ω = O/H Cos Ω = A/H Tan Ω = O/A

Tom Love Malone College Fall 2007