Question

solve 8 cos ^4 x-5=0

Answer 1

In order to do this, you must first simplify by reordering the terms.

Answer 2

\[-5+8\cos^4x=0\]

Answer 3

Then we move all the terms containing c to the left, all the other terms to the right.

Answer 4

\[-5+5+8\cos^4x=0+5\]

Answer 5

Then we combine like terms.

Answer 6

-5+5=0

Answer 7

\[0+8\cos^4x=0+5\]

Answer 8

8cos^4x=0+5

Answer 9

Then we divide each side by\[8os^4x\]

Answer 10

We would get \[c=0.625o^{-1}s^{-4}x^{-1}\]

Answer 11

Normally we would simplify but it is already in simplest form...

Answer 12

???

Answer 13

We'll restart from here, up to which is good:
8cos^4x=0+5
so 8cos^4x=5
Divide both sides by 8
\(cos^4(x)=5/8\)
take 4th root:
\(\rm cos(x)=\pm \dfrac{5}{8}^{1/4}\)
The right hand side is numeric and can be evaluated using a calculator (appr.0.9),
and the corresponding x=acos(0.9)=0.48
Now examine the cosine function

Assuming x=0.48 (radians) is a solution (first intersection of line & curve), then
so are \(\pi-x\), \(\pi+x\), and \(2\pi-x\).
These 4 solutions are between 0 and 2pi.
They repeat at every interval of 2pi, since cos(x) is periodic.
So the general solution is
x=\(k\pi \pm 0.48\) (approximate because 0.9 is an approximate answer)
where k\(\in\)Z (all integers)