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cos((7pi)/(2))

$\cos \left(\frac{7 \pi}{2}\right)$

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Evaluate integers raised to rational exponents

Full solution

Q.

\cos \left(\frac{7 \pi}{2}\right)

Identify angle position: Identify the angle and its position on the unit circle. $\cos\left(\frac{7\pi}{2}\right)$ is the cosine of an angle that is $\frac{7}{2}$ halves of $\pi$ radians.
Recognize odd multiple: Recognize that $(7\pi)/(2)$ is an odd multiple of $(\pi)/(2)$ . This means the angle corresponds to a point on the y-axis of the unit circle.
Determine cosine value: Determine the cosine value for angles on the y-axis. $\newline$ Cosine of an angle on the y-axis is $0$ , since cosine represents the $x$ -coordinate on the unit circle.
Calculate cosine: Calculate the cosine value for $(7\pi)/(2)$ . $\newline$ $\cos((7\pi)/(2)) = 0$

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