The equation of the trigonometric graph which is represented below is y= sin(3x). Option b is correct.
What is the equation of the trigonometric graph?
The equation of the trigonometric graph represent the trigonometric function with the help of angles.Two main ways to prepare the sine and cosine function are,
[tex]y=\sin x\\y=\cos x[/tex]
The graph for the given problem is attached below. In this graph, the function varies from -2π/3 to 2π/3.
The function equation of the trigonometric graph for the sine is given as,
[tex]y=\sin x[/tex]
At the value of 2π/3, the equation will be,
[tex]y=\sin\left( \dfrac{2\pi}{3}x\right)[/tex]
Put the left hand side equal to zero, and find the value of x.
[tex]0=\sin\left( \dfrac{2\pi}{3}x\right)[/tex]
The value of sine is zero at 2π. To this function the value of x must be equal to the 3. Thus,
[tex]0=\sin\left( \dfrac{2\pi}{3}(3)\right)\\0=\sin\left( {2\pi}\right)\\0=0[/tex]
Thus, the number 3 need to be write inside the function of sine as,
[tex]y = \sin(3x)[/tex]
Thus, the equation of the trigonometric graph which is represented below is y= sin(3x). Option b is correct.
Learn more about the equation of the graph here;
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