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1+sin ((17 pi)/(2))

$1+\sin \frac{17 \pi}{2}$

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Evaluate rational exponents

Full solution

Q.

1+\sin \frac{17 \pi}{2}

Simplify Angle: First, let's simplify $\sin\left(\frac{17\pi}{2}\right)$ by finding its equivalent angle in the fundamental period of sine, which is between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ .
Subtract Multiples of $2\pi$ : Since the sine function has a period of $2\pi$ , we can subtract multiples of $2\pi$ from $(17\pi)/2$ until we get an angle within the fundamental period.
Calculate Equivalent Angle: $(\frac{17\pi}{2}) - 8\pi = (\frac{17\pi - 16\pi}{2}) = \frac{\pi}{2}$ .
Find Sine Value: Now, we know that $\sin(\frac{\pi}{2}) = 1$ .
Final Answer: So, $\sin\left(\frac{17\pi}{2}\right)$ is the same as $\sin\left(\frac{\pi}{2}\right)$ , which equals $1$ .
Final Answer: So, $\sin\left(\frac{17\pi}{2}\right)$ is the same as $\sin\left(\frac{\pi}{2}\right)$ , which equals $1$ . Finally, we add this to $1$ to get the final answer: $1 + 1 = 2$ .

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