 # If f ( &#x03B8;<!-- θ --> ) = s i n ( &#x03B8;<!-- θ --> ) = Monserrat Sawyer 2022-05-29 Answered
If $f\left(\theta \right)=sin\left(\theta \right)=0.1$, then find $f\left(\theta +\pi \right)=sin\left(\theta +\pi \right)$
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You can do it by using the summation formula for sines
$\mathrm{sin}\left(x+y\right)=\mathrm{sin}\left(x\right)\mathrm{cos}\left(y\right)+\mathrm{sin}\left(y\right)\mathrm{cos}\left(x\right)$
just set $y=\pi$ and you get
$\begin{array}{rl}& \mathrm{sin}\left(x+\pi \right)=\mathrm{sin}\left(x\right)\mathrm{cos}\left(\pi \right)+\mathrm{sin}\left(\pi \right)\mathrm{cos}\left(x\right)\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}=\mathrm{sin}\left(x\right)\left(-1\right)+0\mathrm{cos}\left(x\right)=-\mathrm{sin}\left(x\right)\end{array}$