Posted by satyajeet on Friday, August 23, 2013 at 11:21am.
3 cot ( theta ) = 4 Divide both sides by 3
cot ( theta ) = 4 / 3
sin ( theta ) = + OR - 1 / sqrt [ 1 + cot ( teta ) ^ 2 ]
In this case :
sin ( theta ) = + OR - 1 / sqrt [ 1 + ( 4 / 3 ) ^ 2 ]
sin ( theta ) = + OR - 1 / sqrt ( 1 + 16 / 9 )
sin ( theta ) = + OR - 1 / sqrt ( 9 / 9 + 16 / 9 )
sin ( theta ) = + OR - 1 / sqrt ( 25 / 9 )
sin ( theta ) = + OR - 1 / ( 5 / 3 )
sin ( theta ) = + OR - 3 / 5
cos ( theta ) = + OR - cot ( theta ) / sqrt [ 1 + cot ( teta ) ^ 2 ]
In this case :
cos ( theta ) = + OR - ( 4 / 3 ) / sqrt [ 1 + ( 4 / 3 ) ^ 2 ]
cos ( theta ) = + OR - ( 4 / 3 ) / sqrt ( 1 + 16 / 9 )
cos ( theta ) = + OR - ( 4 / 3 ) / sqrt ( 9 / 9 + 16 / 9 )
cos ( theta ) = + OR - ( 4 / 3 ) / sqrt ( 25 / 9 )
cos ( theta ) = + OR - ( 4 / 3 ) / ( 5 / 3 )
cos ( theta ) = + OR - ( 4 * 3 ) / ( 3 * 5 )
cos ( theta ) = + OR - 4 / 5
cot ( theta ) = cos ( theta ) / sin ( theta )
In quadran I cosine and sine are positive so quotient of cosine and sine will be positive.
In quadran III cosine and sine are negative so quotient of cosine and sine will be positive.
Now you have 2 sets of solutions :
1. In your equation put :
sin ( theta ) = 3 / 5
cos ( theta ) = 4 / 5
2. In your equation put :
sin ( theta ) = - 3 / 5
cos ( theta ) = - 4 / 5
If your e3xpression mean :
5 cos ( theta ) - 2 sin ( theta ) / [ 5 cos ( theta ) ] + 3 sin ( theta )
Solutions will bee :
- 61 / 10
and
11 / 2