engomavaw10b

2023-02-25

How to calculate $\mathrm{sin}\left(-150°\right)$?

objesilo5lr1

Given solution: $\mathrm{sin}\left(-{150}^{\circ }\right)$
$=-\mathrm{sin}\left({150}^{\circ }\right)$
$=-\mathrm{sin}\left({180}^{\circ }-{30}^{\circ }\right)$

$=-\frac{1}{2}$

daneetuhxxtj

Recall the identification of the negative angle.
$\mathrm{sin}\left(-\theta \right)=-\mathrm{sin}\left(\theta \right)$
With this in mind, we can rewrite #sin(-150)# as #-sin(150)#
${150}^{\circ }$ has a reference angle of ${30}^{\circ }$, which means it will have the same trig values as ${30}^{\circ }$
On the Unit Circle, we know the coordinates for ${30}^{\circ }$ are $\left(\frac{\sqrt{3}}{2},\frac{1}{2}\right)$, where the #y#-coordinate is the $\mathrm{sin}$ value.
This implies $\mathrm{sin}\left(-150\right)=-\frac{1}{2}$

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