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Orlov [11]
2 years ago
13

Please help me. It's literally math!

Mathematics
1 answer:
lorasvet [3.4K]2 years ago
5 0

Answer:

see below

Step-by-step explanation:

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

  • ------------------------------------------------------------------------------------------------------

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

  • ---------------------------------------------------------------------------------------------------

#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 2π 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

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