Question

Cos (1+x) = .3 x equals what?

solve for the x variable in this equation.

Answer 1

`x=0.438779`

Explanation:

.
`cos(1+x)=0.3x`

The easiest way to solve this is graphically. Plot two functions:

`y=cos(1+x)` and

`y=0.3x`

as seen in the graphs below:

As you can see, there is only one solution. The two cross at an `x` value of around`0.4`. Now, we can use an iterative process of increasing and decreasing `x` by very small amounts and find the exact value where the problem equation holds.

That value is `x=0.438779` although the digits continue.

If you had wanted to solve the equation mathematically you would have had to use the trigonometric formula:

`cos(a+b)=cosacosb-sinasinb` for the left hand side:

`cos(1)cosx-son(1)sinx=0.3x`

convert it to an equation in complex number domain:

`1/2e^(-ix-i)+1/2e^(ix+i)=0.3x`

and use advanced math skills to solve for `x`.