## Related questions with answers

Question

Graph each function over a one-period interval. $y=1-2 \csc \left(x+\frac{\pi}{2}\right)$

Solution

VerifiedStep 1

1 of 4We are given:

$y=1-2\csc \left(x+\dfrac{\pi}{2}\right)$

Graph the corresponding reciprocal function as shown by the orange dashed curve:

$y=1-2\sin \left(x+\dfrac{\pi}{2}\right)$

Note: The period of $y=c+a\cos b(x-d)$ is $\frac{2\pi}{b}$. Since $b=1$, then the period is: $\frac{2\pi}{1}=2\pi$. This is the graph of $y=-2\sin x$ that is translated $\frac{\pi}{2}$ to the left and translated 1 unit up.

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