Page 55 - Aeronautical Engineer Data Book

42 Aeronautical Engineer’s Data Book

r

y

A

x

Fig. 2.9 Basic trigonometry

Relations between trigonometric functions
2
2
2
2
sin A + cos A = 1 sec A = 1 + tan A
2
2
cosec A = 1 + cot A
sin A = s cos A = c tan A = t
2 1/2
2 –1/2
sin A s (1 – c ) t(1 + t )
2 –1/2
2 1/2
cos A (1 – s ) c (1 + t )
2 1/2
2 1/2
tan A s(1 – s ) (1 – c ) /ct
A is assumed to be in the first quadrant; signs
of square roots must be chosen appropriately in
other quadrants.
Addition formulae
sin(A ± B) = sin A cos B ± cos A sin B
cos(A ± B) = cos A cos B 7 sin A sin B
tan A ± tan B
tan(A ± B) = 3 3
1
7 tan A tan B
Sum and difference formulae
1
sin A + sin B = 2 sin 1 2 3 3 (A + B) cos (A – B)
3 3
2
sin A – sin B = 2 cos 1 2 3 3 (A + B) sin (A – B)
1
3 3
2
1
cos A + cos B = 2 cos 1 2 3 3 (A + B) cos (A – B)
3 3
2
cos A – cos B = 2 sin 1 2 3 3 (A + B) sin (B – A)
1
3 3
2