1.06 SINUSOIDAL GRAPH VERTICAL SHIFT
What is the period of the function f(x)=cos10x

The cosine function is the trigonometric function, so it is known as the periodic function.

The period of the given function is π/5. The option 4 is the correct option.

What is the period of the cosine function?

The cosine function is the trigonometric function, hence it is known as the periodic function.

The period of a function is the total interval in which the function repeats itself over and over again the of the function for a complete cycle. If,

[tex]f(x)=A\cos(Bx+C)+D[/tex]

Then the period of the cosine function can be given as,

[tex]I=\dfrac{2\pi}{|B|}[/tex]

Given information-

The given function in the problem is,

[tex]f(x)=\cos(10x)[/tex]

The above function is the cosine function. Let a cosine function of in with values of [tex]x[/tex] 0 to 2π.

Now the period of the periodic function is the interval of [tex]x[/tex] values in which the the cycle of graph repeats itself in both directions.

Compare the given function with above equation we get,

[tex]B=10[/tex]

Thus the period of the [tex]\cos (10x)[/tex] is,

[tex]I=\dfrac{2\pi}{|10|}\\I=\dfrac{\pi}{|5|}\\I=\dfrac{\pi}{5}\\[/tex]

Hence the period of the given function is π/5. Thus the option 4 is the correct option.

Learn more about the period of the function here;

https://brainly.com/question/4599903

Answer:

○ [tex]\displaystyle \frac{\pi}{5}[/tex]

Explanation:

[tex]\displaystyle \boxed{f(x) = sin\:(10x + \frac{\pi}{2})} \\ \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{20}} \hookrightarrow \frac{-\frac{\pi}{2}}{10} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{5}} \hookrightarrow \frac{2}{10}\pi \\ Amplitude \hookrightarrow 1[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{\frac{\pi}{5}} \hookrightarrow \frac{2}{10}\pi \\ Amplitude \hookrightarrow 1[/tex]

From the information above, you have your answer.

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