Which of the following is equivalent to tan ((pi)/(5)) ? tan(-(pi)/(5)) tan ((9pi)/(5)) tan ((4pi)/(5)) tan(-(9pi)/(5))

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 + kπ) for any integer k.Comparison with Original Angle: Compare the given angles with the original angle (π/5) using the periodicity of the tangent function. We need to find an angle that differs from (π/5) by an integer multiple of π.Analysis: tan(-(π/5)): Analyze the first option: tan(-(π/5)). The tangent function is odd, which means tan(-θ) = -tan(θ). Therefore, tan(-(π/5)) is not equivalent to tan((π/5)) because it will have the opposite sign.Analysis: tan((9π/5)): Analyze the second option: tan((9π/5)). Using the periodicity of the tangent function, we can subtract π from (9π/5) to see if it is equivalent to (π/5). tan((9π/5)) = tan((9π/5) - π) = tan((9π/5) - (5π/5)) = tan((4π/5)). This is not equivalent to tan((π/5)).Analysis: tan((4π/5)): Analyze the third option: tan((4π/5)). This angle is not equivalent to (π/5) because it is not an integer multiple of π away from (π/5).Analysis: tan(-(9π/5)): Analyze the fourth option: tan(-(9π/5)). Using the periodicity of the tangent function, we can add π to (-(9π/5)) to see if it is equivalent to (π/5). tan(-(9π/5)) = tan(-(9π/5) + π) = tan(-(9π/5) + (5π/5)) = tan(-(4π/5)). This is not equivalent to tan((π/5)) because it is not an integer multiple of π away from (π/5).Conclusion: Conclusion. None of the given options are equivalent to tan((π/5)) because none of them are an integer multiple of π away from (π/5).

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Which of the following is equivalent to
tan ((pi)/(5)) ?

tan(-(pi)/(5))

tan ((9pi)/(5))

tan ((4pi)/(5))

tan(-(9pi)/(5))

Which of the following is equivalent to $\tan \frac{\pi}{5}$ ? $\newline$ $\tan \left(-\frac{\pi}{5}\right)$ $\newline$ $\tan \frac{9 \pi}{5}$ $\newline$ $\tan \frac{4 \pi}{5}$ $\newline$ $\tan \left(-\frac{9 \pi}{5}\right)$

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Math Problems

Algebra 1

Multiplication with rational exponents

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Q. Which of the following is equivalent to

\tan \frac{\pi}{5}

\newline

\tan \left(-\frac{\pi}{5}\right)

\newline

\tan \frac{9 \pi}{5}

\newline

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

\newline

\tan \left(-\frac{9 \pi}{5}\right)

Periodicity of Tangent Function: Understand the periodicity of the tangent function. The tangent function has a period of $\pi$ , which means that $\tan(\theta) = \tan(\theta + k\pi)$ for any integer $k$ .
Comparison with Original Angle: Compare the given angles with the original angle $(\pi/5)$ using the periodicity of the tangent function. $\newline$ We need to find an angle that differs from $(\pi/5)$ by an integer multiple of $\pi$ .
Analysis: $\tan\left(-\left(\frac{\pi}{5}\right)\right)$ : Analyze the first option: $\tan\left(-\left(\frac{\pi}{5}\right)\right)$ . The tangent function is odd, which means $\tan(-\theta) = -\tan(\theta)$ . Therefore, $\tan\left(-\left(\frac{\pi}{5}\right)\right)$ is not equivalent to $\tan\left(\frac{\pi}{5}\right)$ because it will have the opposite sign.
Analysis: $\tan\left(\frac{9\pi}{5}\right)$ : Analyze the second option: $\tan\left(\frac{9\pi}{5}\right)$ . Using the periodicity of the tangent function, we can subtract $\pi$ from $\frac{9\pi}{5}$ to see if it is equivalent to $\frac{\pi}{5}$ . $\tan\left(\frac{9\pi}{5}\right) = \tan\left(\frac{9\pi}{5} - \pi\right) = \tan\left(\frac{9\pi}{5} - \frac{5\pi}{5}\right) = \tan\left(\frac{4\pi}{5}\right)$ . This is not equivalent to $\tan\left(\frac{\pi}{5}\right)$ .
Analysis: $\tan\left(\frac{4\pi}{5}\right)$ : Analyze the third option: $\tan\left(\frac{4\pi}{5}\right)$ . This angle is not equivalent to $\left(\frac{\pi}{5}\right)$ because it is not an integer multiple of $\pi$ away from $\left(\frac{\pi}{5}\right)$ .
Analysis: $\tan\left(-\left(\frac{9\pi}{5}\right)\right)$ : Analyze the fourth option: $\tan\left(-\left(\frac{9\pi}{5}\right)\right)$ . Using the periodicity of the tangent function, we can add $\pi$ to $\left(-\left(\frac{9\pi}{5}\right)\right)$ to see if it is equivalent to $\left(\frac{\pi}{5}\right)$ . $\tan\left(-\left(\frac{9\pi}{5}\right)\right) = \tan\left(-\left(\frac{9\pi}{5}\right) + \pi\right) = \tan\left(-\left(\frac{9\pi}{5}\right) + \left(\frac{5\pi}{5}\right)\right) = \tan\left(-\left(\frac{4\pi}{5}\right)\right)$ . This is not equivalent to $\tan\left(\frac{\pi}{5}\right)$ because it is not an integer multiple of $\pi$ away from $\left(\frac{\pi}{5}\right)$ .
Conclusion: Conclusion. $\newline$ None of the given options are equivalent to $\tan\left(\frac{\pi}{5}\right)$ because none of them are an integer multiple of $\pi$ away from $\frac{\pi}{5}$ .