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justaguide eNotes educator| Certified Educator

We have to solve 5 sin x = 4 cos x

5 sin x = 4 cos x

=> sin x / cos x = 4/5

=> tan x = (4/5)

=> x = arc tan (4/5)

Therefore x = arc tan (4/5) + n*pi

giorgiana1976 | Student

This is an homogenous equation and we'll create the tangent function to solve it

5sinx=4cosx

We'll divide by 5:

sin x = ( 4/5) cos x

Now, we'll create the tangent function by dividing both sides by cos x:

sinx/cosx = 4/5

tan x= 4/5

We've get an elementary equation:

x = arctan (4/5) + k*pi

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