Question

How is inverse sine of -1/square root of 5 = 206.6 and 333.4?

Answer 1

Answer on Question #58561 – Math – Trigonometry

Question

How is inverse sine of -1/square root of $5 = 206.6$ and 333.4?

Solution

The Inverse sine of -1/square root of 5 is approximately equal to $-0.46$ or $-26.6{}^{\circ}$, but $-26.6{}^{\circ}$ is the same as $333.4{}^{\circ}$, because $360{}^{\circ} - 26.6{}^{\circ} = 333.4{}^{\circ}$ and we know the inverse sine is defined to be the inverse of the restricted sine function $\sin x$, where $-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$.

The domain of the inverse sine function $\sin^{-1}x$ is $[-1, 1]$, its range is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$.

Answer: $333.4{}^{\circ}$

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