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blagie [28]
3 years ago
8

Explain why sin^-1(sin(3pi/4))=/=3pi/4 when y=sin x and y=sin^-1 x are inverses.

Mathematics
2 answers:
Strike441 [17]3 years ago
6 0
Y=arcsin(sin(π/4))
The exact value of <span><span>sin <span>(<span>π/4</span>) </span></span>sin </span><span>is </span><span><span><span>√2</span>/</span><span>2
</span></span>y=<span>arcsin<span>(<span><span>√2/</span>2</span><span>)
</span></span></span>The exact value of <span><span>arcsin<span>(<span><span>√2/ </span>2</span>) y</span></span></span>=π/4y=π/4

Interchange the variables.<span>x=<span><span>π/4
</span></span></span>
shtirl [24]3 years ago
3 0

We are given trigonometry expression.

\sin^{-1}(\sin(\frac{3\pi}{4}))\neq \frac{3\pi}{4}

when inverse of y=\sin x is y=\sin^{-1}x

Inverse function gives principle value of angle.

Here we have sin inverse function whose principle value is -\frac{\pi}{2}\leq \theta \leq \frac{\pi}{2}

The value of y must be lie between principle value. This changes because of exact value of sine. If we find \sin(3\pi/4)=\frac{1}{\sqrt{2}}

As we know \sin(\frac{\pi}{4})=\frac{1}{\sqrt{2}}

Thus, The principle value are not same.

Hence, \sin^{-1}(\sin(\frac{3\pi}{4}))\neq \frac{3\pi}{4}

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