Chaya Galloway

## Answered question

2021-08-22

If $f\left(\theta \right)=\mathrm{csc}\theta$ and $f\left(a\right)=2,$ find the exact value of:
a) $f\left(-a\right)$
b) $f\left(a\right)+f\left(a+2\pi \right)+f\left(a+4\pi \right)$

### Answer & Explanation

un4t5o4v

Skilled2021-08-23Added 105 answers

Step 1
Part (a)
Now,
$f\left(-a\right)=\mathrm{csc}\left(-a\right)$
$=-\mathrm{csc}\left(a\right)$
$=-f\left(a\right)$
$=-2$
Step 2
Part (b)
Now,
$f\left(a\right)+f\left(a+2\pi \right)+f\left(a+4\pi \right)=\mathrm{csc}\left(a\right)+\mathrm{csc}\left(a+2\pi \right)+\mathrm{csc}\left(a+4\pi \right)$
$=\mathrm{csc}\left(a\right)+\mathrm{csc}\left(a\right)+\mathrm{csc}\left(a\right)+\mathrm{csc}\left(a\right)$
$=3\mathrm{csc}\left(a\right)$
$=3f\left(a\right)$
$=3\left(2\right)$
$=6$

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