Compute inverse functions to four significant digits.
cos^2x=3-5cosx
rewrite it as..
cos^2x + 5cosx -3=0
now you have a quadratic, solve for cos x using the equation
cosx=(-5 -+ sqrt (25 +12)/2
To find the inverse function, let's first solve for cos(x) in the quadratic equation cos^2x + 5cosx - 3 = 0.
Using the quadratic formula:
cos(x) = (-5 ± √(25 + 12)) / 2
cos(x) = (-5 ± √37) / 2
Now, to find the inverse function, we need to swap the x and y variables and solve for y:
y = (-5 ± √37) / 2
Therefore, the inverse functions are:
cos^(-1)((-5 + √37) / 2) and cos^(-1)((-5 - √37) / 2)
These inverse functions give the input value of x when the output value of cos(x) is equal to (-5 + √37) / 2 or (-5 - √37) / 2, respectively.