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(1+sin ((10 pi)/(2)))

$\left(1+\sin \frac{10 \pi}{2}\right)$

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Evaluate rational exponents

Full solution

Q.

\left(1+\sin \frac{10 \pi}{2}\right)

Simplify angle for sine: First, let's simplify the angle for the sine function. The sine function has a period of $2\pi$ , so we can subtract multiples of $2\pi$ to find an equivalent angle. $\newline$ $(10\pi/2) = 5\pi$ , and since $5\pi$ is an odd multiple of $\pi$ , $\sin(5\pi)$ is the same as $\sin(\pi)$ .
Find sine value: Now, we know that $\sin(\pi) = 0$ because $\pi$ corresponds to $180$ degrees on the unit circle, and the sine of $180$ degrees is $0$ .
Replace in expression: So, we replace $\sin(5\pi)$ with $0$ in our original expression: $1 + \sin(5\pi) = 1 + 0$ .
Perform addition: Now, just do the simple addition: $1 + 0 = 1$ .

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