Question

Please help me. It's literally math!

Answer 1

Answer:

see below

Step-by-step explanation:

given function: $Cos(x)=\frac{1}{3}$

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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.

$x=arccos\frac{1}{3}$

#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 $\frac{2\pi }{|b|}$.

$\frac{2\pi }{|b|}$

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

$\frac{2\pi }{|1|}$

#6: Solve the equation.

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

$\frac{2\pi }{1}$

- 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 $n$