Trigonometry (Continued)

Cosine Formula (Cosine Rule)

Theorem:

If ABC is a triangle with sides a = BC, b = CA, c = AB, then prove that

In figure (i),

A < 90^o

But from D BAE, we have

In figure (ii),

A > 90^o

But from D BAE, we have

In figure(iii),

From (i), (ii) and (iii), we conclude that

Similarly, b² = c² + a² - 2 ca cos B

Example:

Suggested answer:

Dividing throughout by 2abc, we get

Get FREE Live Tutoring

(No credit card required)

Click to get customer service, technical support and subscription help.

Get One Month Free!
When you refer a friend

	Introduction
	Co-terminal Angles
	Theorem 1
	Theorem 2
	Theorem 3
	Theorem 4
	Sine Formula (Sine Rule)
	Cosine Formula (Cosine Rule)
	Projection Formula
	Napier's Analogy
	Area of a triangle
	Hero's Formula
	Half-Angle Formulae
	Solution of triangles
	Heights and Distances
	Inverse Trigonometric Functions
	Summary
Animations
	Graphs of Inverse Trigonometric functions

Subjects
English
Math
Geometry