How do you evaluate $cos 870$ $cos 870$ ?

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How do you evaluate $cos 870$ $cos 870$ ?

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Answer 1 · 2016-10-05T14:51:10

${cos 870}^{o} = - \frac{\sqrt{3}}{2}$ $cos870^o=-sqrt3/2$

Explanation:

As trigonometric ratios get repeated over a cycle over $2 π$ $2pi$ or $360^{o}$ $360^o$ .

Hence ${cos 870}^{o} = cos (360^{o} \times 2 + 150^{o}) = {cos 150}^{o}$ $cos870^o=cos(360^o xx2+150^o)=cos150^o$

Further as $cos (180^{o} - A) = - cos A$ $cos(180^o-A)=-cosA$

${cos 870}^{o} = {cos 150}^{o} = cos (180^{o} - 30^{o}) = - {cos 30}^{o} = - \frac{\sqrt{3}}{2}$ $cos870^o=cos150^o=cos(180^o-30^o)=-cos30^o=-sqrt3/2$

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