Which of the following is not equivalent to tan ((pi)/(4)) ? tan ((7pi)/(4)) tan ((9pi)/(4)) tan ((5pi)/(4)) tan(-(7pi)/(4))

Periodicity of Tangent Function: Understand the periodicity of the tangent function. The tangent function has a period of π, which means that tan(θ) = tan(θ + nπ) for any integer n.Evaluate tan((pi)/(4)): Evaluate tan((pi)/(4)). The value of tan((pi)/(4)) is 1 because the tangent of an angle in a right triangle with equal sides is 1.Evaluate tan((7pi)/(4)): Evaluate tan((7pi)/(4)). Using the periodicity of the tangent function, tan((7pi)/(4)) is equivalent to tan((7pi)/(4) - 2π) which is tan(-(pi)/(4)). Since tan(-θ) = -tan(θ), tan(-(pi)/(4)) = -tan((pi)/(4)) = -1.Evaluate tan((9pi)/(4)): Evaluate tan((9pi)/(4)). Using the periodicity of the tangent function, tan((9pi)/(4)) is equivalent to tan((9pi)/(4) - 2π) which is tan((pi)/(4)). Therefore, tan((9pi)/(4)) = tan((pi)/(4)) = 1.Evaluate tan((5pi)/(4)): Evaluate tan((5pi)/(4)). Using the periodicity of the tangent function, tan((5pi)/(4)) is equivalent to tan((5pi)/(4) - π) which is tan((pi)/(4)). Therefore, tan((5pi)/(4)) = tan((pi)/(4)) = 1.Evaluate tan(-(7pi)/(4)): Evaluate tan(-(7pi)/(4)). Using the periodicity of the tangent function, tan(-(7pi)/(4)) is equivalent to tan(-(7pi)/(4) + 2π) which is tan((pi)/(4)). Therefore, tan(-(7pi)/(4)) = tan((pi)/(4)) = 1.Determine Non-Equivalent Option: Determine which option is not equivalent to tan((pi)/(4)). From the previous steps, we have determined that tan((7pi)/(4)) is the only option that is not equivalent to tan((pi)/(4)) because it equals -1, while all the other options equal 1.

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Which of the following is not equivalent to
tan ((pi)/(4)) ?

tan ((7pi)/(4))

tan ((9pi)/(4))

tan ((5pi)/(4))

tan(-(7pi)/(4))

Which of the following is not equivalent to $\tan \frac{\pi}{4}$ ? $\newline$ $\tan \frac{7 \pi}{4}$ $\newline$ $\tan \frac{9 \pi}{4}$ $\newline$ $\tan \frac{5 \pi}{4}$ $\newline$ $\tan \left(-\frac{7 \pi}{4}\right)$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Which of the following is not equivalent to

\tan \frac{\pi}{4}

\newline

\tan \frac{7 \pi}{4}

\newline

\tan \frac{9 \pi}{4}

\newline

\tan \frac{5 \pi}{4}

\newline

\tan \left(-\frac{7 \pi}{4}\right)

Periodicity of Tangent Function: Understand the periodicity of the tangent function. The tangent function has a period of $\pi$ , which means that $\tan(\theta) = \tan(\theta + n\pi)$ for any integer $n$ .
Evaluate $\tan\left(\frac{\pi}{4}\right)$ : Evaluate $\tan\left(\frac{\pi}{4}\right)$ . $\newline$ The value of $\tan\left(\frac{\pi}{4}\right)$ is $1$ because the tangent of an angle in a right triangle with equal sides is $1$ .
Evaluate $\tan\left(\frac{7\pi}{4}\right)$ : Evaluate $\tan\left(\frac{7\pi}{4}\right)$ . Using the periodicity of the tangent function, $\tan\left(\frac{7\pi}{4}\right)$ is equivalent to $\tan\left(\frac{7\pi}{4} - 2\pi\right)$ which is $\tan\left(-\frac{\pi}{4}\right)$ . Since $\tan(-\theta) = -\tan(\theta)$ , $\tan\left(-\frac{\pi}{4}\right)$ = $-\tan\left(\frac{\pi}{4}\right)$ = $-1$ .
Evaluate $\tan\left(\frac{9\pi}{4}\right)$ : Evaluate $\tan\left(\frac{9\pi}{4}\right)$ . Using the periodicity of the tangent function, $\tan\left(\frac{9\pi}{4}\right)$ is equivalent to $\tan\left(\frac{9\pi}{4} - 2\pi\right)$ which is $\tan\left(\frac{\pi}{4}\right)$ . Therefore, $\tan\left(\frac{9\pi}{4}\right)$ = $\tan\left(\frac{\pi}{4}\right)$ = $1$ .
Evaluate $\tan\left(\frac{5\pi}{4}\right)$ : Evaluate $\tan\left(\frac{5\pi}{4}\right)$ . Using the periodicity of the tangent function, $\tan\left(\frac{5\pi}{4}\right)$ is equivalent to $\tan\left(\frac{5\pi}{4} - \pi\right)$ which is $\tan\left(\frac{\pi}{4}\right)$ . Therefore, $\tan\left(\frac{5\pi}{4}\right) = \tan\left(\frac{\pi}{4}\right) = 1$ .
Evaluate $\tan\left(-\frac{7\pi}{4}\right)$ : Evaluate $\tan\left(-\frac{7\pi}{4}\right)$ . Using the periodicity of the tangent function, $\tan\left(-\frac{7\pi}{4}\right)$ is equivalent to $\tan\left(-\frac{7\pi}{4} + 2\pi\right)$ which is $\tan\left(\frac{\pi}{4}\right)$ . Therefore, $\tan\left(-\frac{7\pi}{4}\right) = \tan\left(\frac{\pi}{4}\right) = 1$ .
Determine Non-Equivalent Option: Determine which option is not equivalent to $\tan\left(\frac{\pi}{4}\right)$ . From the previous steps, we have determined that $\tan\left(\frac{7\pi}{4}\right)$ is the only option that is not equivalent to $\tan\left(\frac{\pi}{4}\right)$ because it equals $-1$ , while all the other options equal $1$ .