SOLUTION: 5 cos @ + 12 sin @ = 13 Find. tan @ = ?

Question 1062997: 5 cos @ + 12 sin @ = 13
Find. tan @ = ?
Answer by ikleyn(52806) (Show Source): You can put this solution on YOUR website!
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5 cos @ + 12 sin @ = 13
Find tan @ = ?
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Answer. = .

Solution

Let x = .  Then  =  = .


Then the original equation is equivalent to

 = 13,   or

5x - 13 = .   (1)

To solve (1), square both sides. You will get

 = 144*(1-x^2),

25x^2 - 130x + 169 = 144 - 144x^2,

25x^2 + 144x^2 - 130x + 169 - 144 = 0,

169x^2 - 130x + 25 = 0,

 = 0,

---->  13x - 5 = 0  ---->  13x = 5  ---->  x = .


Thus you get  = .


Then  =  =  =  =  = .


Now   =  =  = .

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