Respuesta :
Answer:
see below
Step-by-step explanation:
given function: [tex]Cos(x)=\frac{1}{3}[/tex]
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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 [tex]x[/tex] from inside the cosine.
[tex]x=arccos\frac{1}{3}[/tex]
#2: Evaluate
[tex]x=1.23095941[/tex]
#3: The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from [tex]2[/tex]π to find the solution in the fourth quadrant.
[tex]x=2(3.14159265)-1.23095941[/tex]
#4: Simplify the equation above.
- Multiply [tex]2[/tex] by [tex]3.14159265[/tex]
[tex]x=6.2831853-1.23095941[/tex]
- Subtract [tex]1.23095941[/tex] from [tex]6.2831853[/tex]
[tex]x=5.05222588[/tex]
#5: Find the period.
- The period of the function can be calculated using [tex]\frac{2\pi }{|b|}[/tex].
[tex]\frac{2\pi }{|b|}[/tex]
- Replace [tex]b[/tex] with [tex]1[/tex] in the formula for period.
[tex]\frac{2\pi }{|1|}[/tex]
#6: Solve the equation.
- The absolute value is the distance between a number and zero. The distance between [tex]0[/tex] and [tex]1[/tex] is [tex]1[/tex].
[tex]\frac{2\pi }{1}[/tex]
- Divide [tex]2\pi[/tex] by [tex]1.[/tex]
[tex]2\pi[/tex]
The period of the [tex]cos(x)[/tex] function is [tex]2\pi[/tex] so values will repeat every [tex]2\pi[/tex] radians in both directions.
[tex]x=1.23095941+2\pi n,5.05222588+2\pi n[/tex], for any integer [tex]n[/tex]
