Basic Trigonometric Functions (Solving Problems with Triangles)

Basic Trigonometric Functions

(Solving Problems with Triangles)

Pythagorean Theorem

1Pythagorean Theorem
      a² + b² = c²
a = side of right triangle
b = side of right triangle
c = hypotenuse (The hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle.)

                                                                                                                                                                                                                                         

Sine, Cosine and Tangent for Right-Angled Triangles

"Opposite" is opposite to the angle θ
"Adjacent" is adjacent (next to) to the angle θ
"Hypotenuse" is the long one

2Sine	sin θ =	Opposite
		Hypotenuse
3Cosine	cos θ =	Adjacent
		Hypotenuse
4Tangent	tan θ =	Opposite
		Adjacent

                                                                                                                                                                                                                                         

Laws of Sines and Cosines for Any Triangle

5Sine Rule   for finding a missing angle when given an angle and two sides, or for finding a missing side when given two angles and one side.

Formula:

a		b		c
sin A	=	sin B	=	sin C

6Cosine Rule    for finding an angle measure when given all side lengths or finding a missing side when given the other sides and one angle measure.

Formulas:
     a² = b² + c² - 2bc cos A
     b² = a² + c² - 2ac cos B
     c² = a² + b² - 2ab cos C

                                                                                                                                                                                                                                         

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