What is 5/8 divided by 1/16, and then once you solve that can you solve 5/8 divided by 1/32?

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Ответ:

Mofurd

10.04.2022

Mathematics

The expression that represents all quadrantal angkes is $\phi = n\frac{\pi}{2}$ where is an integer.

Step-by-step explanation:

Recall that the quadrantal angles are those coterminal with , $\frac{\pi}{2}$ , $\pi$ and $\frac{3\pi}{2}$ . Now, notice that all of them can be written as integer multiples of $\frac{\pi}{2}$ :

$0 = 0\cdot \frac{\pi}{2}$ $\frac{\pi}{2} = 1\cdot \frac{\pi}{2}$ $\pi = 2\cdot \frac{\pi}{2}$ $\frac{3\pi}{2} = 3\cdot \frac{\pi}{2}$

Then, if we add to each one of the listed above angles an integer multiple of $2\pi$ we get

$0\cdot \frac{\pi}{2}+2n\pi = \frac{0\pi +4n\pi}{2} = 4n\frac{\pi}{2}$ $1\cdot \frac{\pi}{2} + 2n\pi = \frac{\pi +4n\pi}{2} = (4n+1)\frac{\pi}{2}$ $2\cdot \frac{\pi}{2}+ 2n\pi = \frac{2\pi +4n\pi}{2} = (4n+2)\frac{\pi}{2}$ $3\cdot \frac{\pi}{2}+ 2n\pi = \frac{3\pi +4n\pi}{2} = (4n+3)\frac{\pi}{2}$

But the numbers of the form , 4n+1 , 4n+2 and 4n+3 where is an integer, encompass all integers. Thus, all quadrantal angles can be written as

$\phi = n\frac{\pi}{2}$ where is an integer.

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