Page 56 - Aeronautical Engineer Data Book

Fundamental dimensions and units 43
Product formulae
sin A sin B = 1 2 3 3 {cos(A – B) – cos(A + B)}
cos A cos B = 1 2 3 3 {cos(A – B) + cos(A + B)}
1 3 3 {sin(A – B) + sin(A + B)}
sin A cos B = 2
Powers of trigonometric functions
1
2
sin A = 3 – 1 3 3 cos 2A
3
2 2
1
cos 2 A = 3 +
1 3 3 cos 2A
3
2 2
1
3
3
sin A = 3 sin A – sin 3A
3
3 3
4 4
3
cos 3 A = 3 cos A + 1 3 3 cos 3A
3
4 4
2.8.15 Co-ordinate geometry
Straight-line
General equation
ax + by + c = 0
m = gradient
c = intercept on the y-axis
Gradient equation
y = mx + c
Intercept equation
x y A = intercept on the x-axis
3
3 3 +
3 = 1
A B B = intercept on the y-axis
Perpendicular equation
x cos + y sin = p
p = length of perpendicular from the
origin to the line
= angle that the perpendicular makes
with the x-axis
The distance between two points P(x , y ) and
1
1
, y ) and is given by:
Q(x 2 2
PQ = � � ) + (�)� 2
�
2
–
y
–
x
y
x
(
2
1
1
2
The equation of the line joining two points (x ,
1
) and (x , y ) is given by:
y 1 2 2
y – y 1
3
3 = x – x 1
3 3
y – y 2 x – x 2
1
1