How to solve the equation $x = 45 \cos(x)$?
I have tried online graphing charts (e.g. desmos) and online calculators (e.g. wolframalpha) to find the root of the above equation. I am getting multiple solutions for the given equation and below is the partial list:
The problem is that, when I plug in these values in the given equation, these values don't satisfy it.
On
When you tried the graphing approach, what did it look like? For my Desmos graph I plotted the left and right sides of your equation as separate functions, that is, one function was plotted by $y = x$ and the other by $y = 45 \cos(x).$ My graph looked like this:
Notice that the cosine function on this graph goes through multiple cycles between $x = 0$ and $x = 20.$ That's because if you want the input value of the mathematical cosine function to represent an angle, you have to measure that angle in radians, as several other people have already pointed out.
If you are thinking of the "cosine" function that takes the number of degrees in an angle and produces a sinusoidal function $f$ that decreases from
$f(0)=1$ to $f(90) = 0,$
you can tell Desmos to plot $y=\cos\left(\frac\pi{180}x\right),$
or you can go into its settings and select "Degrees" instead of "Radians".
Making either of these changes, I get a graph like this:
Please note that all these solutions are in radians.