Please help me. It's literally math! Find the exact two values for this problem in radians. Cos x = 1/3

Question

Please help me. It's literally math!

Find the exact two values for this problem in radians.


`Cos x = 1/3`

Answer 1

see below

Explanation:

given function:
`Cos(x)=(1)/(3)`

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Cosine - (In a right triangle, the ratio of the length of the adjacent side to the length of the hypotenuse.)

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#1: Take the inverse cosine of both sides of the equation to extract
`x` from inside the cosine.

`x=arccos(1)/(3)`

#2: Evaluate

`x=1.23095941`

#3: The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from
`2`π to find the solution in the fourth quadrant.

`x=2(3.14159265)-1.23095941`

#4: Simplify the equation above.

- Multiply
`2` by
`3.14159265`

`x=6.2831853-1.23095941`

- Subtract
`1.23095941` from
`6.2831853`

`x=5.05222588`

#5: Find the period.

- The period of the function can be calculated using
`(2\pi )/(|b|)`.

`(2\pi )/(|b|)`

- Replace
`b` with
`1` in the formula for period.

`(2\pi )/(|1|)`

#6: Solve the equation.

- The absolute value is the distance between a number and zero. The distance between
`0` and
`1` is
`1`.

`(2\pi )/(1)`

- Divide
`2\pi` by
`1.`

`2\pi`

The period of the
`cos(x)` function is
`2\pi` so values will repeat every
`2\pi` radians in both directions.

`x=1.23095941+2\pi n,5.05222588+2\pi n`, for any integer
`n`