Find the exact value of $$\text{arcsec}(-\sqrt{2})$$

Haven Kerr
2022-09-26
Answered

Find the exact value of $$\text{arcsec}(-\sqrt{2})$$

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moderrockblog09

Answered 2022-09-27
Author has **7** answers

Solution:

$$\mathrm{sec}(\pi -\frac{\pi}{4})\phantom{\rule{0ex}{0ex}}=\mathrm{sec}(-\frac{\pi}{4})\phantom{\rule{0ex}{0ex}}=-\sqrt{2}\phantom{\rule{0ex}{0ex}}\mathrm{sec}(\pi -\frac{\pi}{4})=\mathrm{sec}(\frac{3\pi}{4})=-\sqrt{2}\phantom{\rule{0ex}{0ex}}\therefore \text{arcsec}(-\sqrt{2})=\frac{3\pi}{4}$$

$$\mathrm{sec}(\pi -\frac{\pi}{4})\phantom{\rule{0ex}{0ex}}=\mathrm{sec}(-\frac{\pi}{4})\phantom{\rule{0ex}{0ex}}=-\sqrt{2}\phantom{\rule{0ex}{0ex}}\mathrm{sec}(\pi -\frac{\pi}{4})=\mathrm{sec}(\frac{3\pi}{4})=-\sqrt{2}\phantom{\rule{0ex}{0ex}}\therefore \text{arcsec}(-\sqrt{2})=\frac{3\pi}{4}$$

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