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Vanyuwa [196]
3 years ago
5

Calculating cos-1 ( help is gladly appreciated :) )

Mathematics
1 answer:
Alekssandra [29.7K]3 years ago
4 0

Answer:

\frac{3\pi}{4}

(Assuming you want your answer in radians)

If you want the answer in degrees just multiply your answer in radians by \frac{180^\circ}{\pi} giving you:

\frac{3\pi}{4} \cdot \frac{180^\circ}{\pi}=\frac{3(180)}{4}=135^{\circ}.

We can do this since \pi \text{ rad }=180^\circ (half the circumference of the unit circle is equivalent to 180 degree rotation).

Step-by-step explanation:

\cos^{-1}(x) is going to output an angle measurement in [0,\pi].

So we are looking to solve the following equation in that interval:

\cos(x)=-\frac{\sqrt{2}}{2}.

This happens in the second quadrant on the given interval.

The solution to the equation is \frac{3\pi}{4}.

So we are saying that \cos(\frac{3\pi}{4})=\frac{-\sqrt{2}}{2} implies \cos^{-1}(\frac{-\sqrt{2}}{2})=\frac{3\pi}{4} since \frac{3\pi}{4} \in [0,\pi].

Answer is \frac{3\pi}{4}.

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