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Question Number 73757 by Maclaurin Stickker last updated on 15/Nov/19

$$\cos 70°+\sin 200°=?$$

Commented by mathmax by abdo last updated on 15/Nov/19

$${70}^o=\frac{70\pi }{180}=\frac{7\pi }{18}and{200}^o=\frac{200\pi }{180}=\frac{20\pi }{18}\Rightarrow$$$$cos\left({70}^o\right)+sin\left({200}^o\right)=cos\left(\frac{7\pi }{18}\right)+sin\left(\frac{20\pi }{18}\right)$$$$\frac{7\pi }{18}+\frac{20\pi }{18}=\frac{27\pi }{18}=\frac{3\pi }{2}\Rightarrow sin\left(\frac{20\pi }{18}\right)=sin(\frac{3\pi }{2}-\frac{7\pi }{18})$$$$=sin(\pi +\frac{\pi }{2}-\frac{7\pi }{18})=-sin(\frac{\pi }{2}-\frac{7\pi }{18})=-cos\left(\frac{7\pi }{18}\right)\Rightarrow$$$$cos\left({70}^o\right)+cos\left({200}^o\right)=0$$

Answered by ajfour last updated on 15/Nov/19

$$=\sin 20°-\sin 20°=0$$

Commented by Maclaurin Stickker last updated on 15/Nov/19

$$Whyitissin20°?$$

Commented by ajfour last updated on 15/Nov/19

$$\cos \left(70°\right)=\cos (90°-20°)=\sin 20°$$

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