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# Trigonometry

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If n is an integer, n * 180 degrees represents an integer multiple of 180 degrees, (2n + 1) * 90 degrees represents an odd integer multiple of 90 degrees, and so on. Decide whether each expression is equal to 0, 1, -1, or is undefined ?

csc[(4n+1) * 90degrees]

Any help provided on this would be very appreciated!

Sep 7, 2018

$$(4n+1)\cdot 90^\circ = n360^\circ + 90^\circ \\ \\ \text{trig functions are all periodic with period }360^\circ \\ \text{so}\csc((4n+1)\cdot 90^\circ) = \csc(90^\circ) \\ \csc(90^\circ) = \dfrac{1}{\sin(90^\circ)} = \dfrac{1}{1} = 1$$