Trigonometry notes

Page 1

Trigonometry

The Theorem of Pythagoras : a^2 + b^2 = c^2

In a right-angled triangle, the area of the square drawn on the hypotenuse is equal to the sum of the areas of the squared drawn on the other two sides.

Sine, Cosine and Tangent ratios : sinA = opp/hyp SOH CAH TOA

cosA =adj/hyp

tanA = opp/adj

Page 2

Trigonometry

The area of a triangle : 1/2 ac sinB or 1/2 bc sinA or 1/2 ab sinC

Area=Half the product of any two sides multiplied by the sine of the angle between them.

area = 1/2 * base * perpendicular height

The Sine rule : a/sinA = b/sinB = c/sinC or sinA/a = sinB/b = sinC/c

The Cosine rule : a^2 = b^2 + c^2 - 2bc cosA or b^2 = c^2 + a^2 - 2ac cosB or c^2 = a^2 + b^2 - 2ab cosC

Area of sector - Length of arc : Area of sector = Q/360' * (pi)r^2

Length of minor arc = Q/360' * 2(pi)r

Page 3

Tigonometry

Ratios of angles greater than 90' :

The four quadrants : The x-axis and y-axis divide a full rotation of 360' into 4 quadrants as shown below.

In the 1st quadrant all (A) are positive, 2nd quadrant sin(S) only positive, 3rd quadrant tan(T) only positive, 4th quadrant cos(C) only positive.