Mary Hammonds

2021-12-26

Find the value of $\mathrm{cos}240\xb0$ .

enhebrevz

Beginner2021-12-27Added 25 answers

Reference angle for 240° is 60°: 240°=180°+60°

$\mathrm{cos}60\xb0=\frac{1}{2}$

As$\mathrm{cos}240\xb0=-\mathrm{cos}60\xb0$ , we have

$\mathrm{cos}240\xb0=-\frac{1}{2}$

As

Rita Miller

Beginner2021-12-28Added 28 answers

Write $\mathrm{cos}240\xb0$ as $\mathrm{cos}(180\xb0+60\xb0)$

Using the summation identity:

$\mathrm{cos}\left(180\xb0\right)\mathrm{cos}\left(60\xb0\right)-\mathrm{sin}\left(180\xb0\right)\mathrm{sin}\left(60\xb0\right)$

Using trivial identity:$\mathrm{cos}180\xb0=(-1),\mathrm{cos}60\xb0=\frac{1}{2},\mathrm{sin}180\xb0=0,\mathrm{sin}60\xb0=\frac{\sqrt{3}}{2}$

$=(-1)\times \frac{1}{2}-0\times \frac{\sqrt{3}}{2}$

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

Using the summation identity:

Using trivial identity:

karton

Expert2022-01-04Added 613 answers

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