Trigonometric Functions and Graphs

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Math › Trigonometric Functions and Graphs

Questions 1 - 10

What is the period of

$\tan \left ( \frac{x}{\pi } \right )$ ?

$\pi^{2}$

$\frac{1}{\pi }$

$2\pi$

$\pi$

Explanation

The period for $\tan(x)$ is $\pi$ . However, if a number is multiplied by , you divide the period $\pi$ by what is being multiplied by . Here, $(1/\pi )$ is being multiplied by . $\pi/(1/\pi )$ equals $\pi^{2}$ .

What is the amplitude of $y=3\sin(2x+5)$ ?

$-\frac{5}{2}$

$-\frac{5}{3}$

Explanation

The amplitude of a wave function like $y=3\sin(2x+5)$ is always going to be the coefficient of the function. In this case, that is .

What is the period of

$\tan \left ( \frac{x}{\pi } \right )$ ?

$\pi^{2}$

$\frac{1}{\pi }$

$2\pi$

$\pi$

Explanation

What is the period of

$\tan \left ( \frac{x}{\pi } \right )$ ?

$\pi^{2}$

$\frac{1}{\pi }$

$2\pi$

$\pi$

Explanation

What is the amplitude of $y=3\sin(2x+5)$ ?

$-\frac{5}{2}$

$-\frac{5}{3}$

Explanation

The amplitude of a wave function like $y=3\sin(2x+5)$ is always going to be the coefficient of the function. In this case, that is .

What is the amplitude of $y=3\sin(2x+5)$ ?

$-\frac{5}{2}$

$-\frac{5}{3}$

Explanation

The amplitude of a wave function like $y=3\sin(2x+5)$ is always going to be the coefficient of the function. In this case, that is .

Which of the given functions has the greatest amplitude?

$2\sin(x)$

$\sin(4x)$

$\sin(x+3)$

$\sin\frac{2\pi }{3}(x+2)$

$\frac{1}{2}\sin(4x)$

Explanation

The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is $2\sin(x)$ .

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.

Which of the given functions has the greatest amplitude?

$2\sin(x)$

$\sin(4x)$

$\sin(x+3)$

$\sin\frac{2\pi }{3}(x+2)$

$\frac{1}{2}\sin(4x)$

Explanation

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.

Which of the given functions has the greatest amplitude?

$2\sin(x)$

$\sin(4x)$

$\sin(x+3)$

$\sin\frac{2\pi }{3}(x+2)$

$\frac{1}{2}\sin(4x)$

Explanation

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.

Simplify the function below:

$f(x)=cos^2(\frac{1}{2}cos^{-1}x)$