# Find the value of \cos240°.

Find the value of $$\displaystyle{\cos{{240}}}°$$.

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enhebrevz
Reference angle for 240° is 60°: 240°=180°+60°
$$\displaystyle{\cos{{60}}}°={\frac{{{1}}}{{{2}}}}$$
As $$\displaystyle{\cos{{240}}}°=-{\cos{{60}}}°$$, we have
$$\displaystyle{\cos{{240}}}°=-{\frac{{{1}}}{{{2}}}}$$
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Rita Miller
Write $$\displaystyle{\cos{{240}}}°$$ as $$\displaystyle{\cos{{\left({180}°+{60}°\right)}}}$$
Using the summation identity:
$$\displaystyle{\cos{{\left({180}°\right)}}}{\cos{{\left({60}°\right)}}}-{\sin{{\left({180}°\right)}}}{\sin{{\left({60}°\right)}}}$$
Using trivial identity: $$\displaystyle{\cos{{180}}}°={\left(-{1}\right)},{\cos{{60}}}°={\frac{{{1}}}{{{2}}}},{\sin{{180}}}°={0},{\sin{{60}}}°={\frac{{\sqrt{{{3}}}}}{{{2}}}}$$
$$\displaystyle={\left(-{1}\right)}\times{\frac{{{1}}}{{{2}}}}-{0}\times{\frac{{\sqrt{{{3}}}}}{{{2}}}}$$
$$\displaystyle=-{\frac{{{1}}}{{{2}}}}$$
karton

The value of $$\cos240°\ is\ -\frac{1}{2}$$

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