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  Trigonometric Formulas
 
 
TRIGONOMETRIC FUNCTIONS
Radius AF = 1
= sin 2 A + cos 2 A = sin A cosec A
= cos A sec A = tan A cot A
Sine A = cos a/cot a = 1/cosec a = cos a tan a = =BC
Cosine A = sin a/tan a = 1/sec a = sin a cot a = =AC
Tangent A = sin A/cos A = 1/cot A = sin A sec A =FD
Cotangent A = cos A/sin A = 1/tan A = cos A cosec A =HG
Secant A = tan A/sin A = 1/cos A =AD
Cosecant A = cot A/cos A = 1/sin A =AG
 
 
RIGHT ANGLED TRIANGLES


a2 = c2 - b2
b2 = c2 - a2
c2 = a2 + b2
Known Required
A B a b c Area
 a,b tan A = a/b tan B = b/a     ab/2
 a,c sin A = a/c cos B = a/c     a/2
 A,a   90o - A   a cot A a/sin A (a2 cot A)/2
 A,b   90o - A b tan a   b/cos A (b2 tan A)/2
 A,c   90o - A c sin a c cos A   (c2 sin 2 A)/4
 
 
OBLIQUE ANGLED TRIANGLES




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

Known Required
A B a b c Area
a,b,c tan 1/2 A = K/(s-a) tan 1/2 B = K/(a-b) tan 1/2 C = K/(s-c)    
a,A,B     180 - (A + B) (a sin B)/sin A (a sin C)/sin A  
a,b,A   sin B = (b sin A)/a     (b sin C) / sin B  
a,b,C tan A = (a sin C)/(b - a cos C)       (ab sin C)/2