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January 22, 2017
Posted by **satyajeet** on Friday, August 23, 2013 at 11:21am.

- maths -
**Bosnian**, Friday, August 23, 2013 at 12:10pm3 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