finding an argumentfind an argument that makes the identity to be true 7sin x=6cos x

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

An identity is true for all values of x, the more appropriate word here would be equation.

We have to find the value of x for which the equation 7*sin x = 6*cos x.

7*sin x = 6*cos x

=> sin x / cos x = 6/7

=> tan x = 6/7

=> x = arc tan(6/7)

=> x = 40.60 degrees

The value of x that makes 7sin x = 6cos x is 40.60 degrees

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

This is an homogenous equation. For solving the equation, we'll have to create the tangent function.

7sinx=6cosx

Knowing that tan x = sin x/cos x, we'll create tangent function by dividing all equation by cos x:

7sin x/cos x - 6 = 0

7tan x - 6 = 0

We'll add 6 both sides:

7tan x = 6

We'll divide by 7:

tan x = 6/7

We've get an elementary equation:

x = arctan (6/7) + k*pi

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