Find the value of \cos240°.

Mary Hammonds 2021-12-26 Answered
Find the value of \(\displaystyle{\cos{{240}}}°\).

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Expert Answer

enhebrevz
Answered 2021-12-27 Author has 5005 answers
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
Answered 2021-12-28 Author has 257 answers
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: \(\displaystyle{\cos{{180}}}°={\left(-{1}\right)},{\cos{{60}}}°={\frac{{{1}}}{{{2}}}},{\sin{{180}}}°={0},{\sin{{60}}}°={\frac{{\sqrt{{{3}}}}}{{{2}}}}\)
\(\displaystyle={\left(-{1}\right)}\times{\frac{{{1}}}{{{2}}}}-{0}\times{\frac{{\sqrt{{{3}}}}}{{{2}}}}\)
\(\displaystyle=-{\frac{{{1}}}{{{2}}}}\)
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karton
Answered 2022-01-04 Author has 8659 answers

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

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