How to find the value of $\cos (120 °)$ ? Solve with steps.

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Solution

Solve for the required value
As, $120 ° = 90 ° + 30 °$
So, $\cos (120 °) = \cos (90 ° + 30 °)$
$\Rightarrow$ $\cos (120 °) = \cos (90 °) \cos (30 °) - \sin (90 °) \sin (30 °)$ $[∵ \cos (a + b) = \cos (a) \cos (b) - \sin (a) \sin (b)]$
$\Rightarrow$ $\cos (120 °) = (0) (\frac{\sqrt{3}}{2}) - (1) (\frac{1}{2})$ $[∵ \cos (90 °) = 0, \sin (90 °) = 1, \cos (30 °) = \frac{\sqrt{3}}{2}, \sin (30 °) = \frac{1}{2}]$
$\Rightarrow$ $\cos (120 °) = - \frac{1}{2}$
Hence, the value of $\cos (120 °)$ is $- \frac{1}{2}$ .

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Q. The steps to solve the equation

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How to find the value of cos120°? Solve with steps.

Solve for the required valueAs, 120°=90°+30°So, cos120°=cos90°+30°⇒cos120°=cos90°cos30°-sin90°sin30° ∵cosa+b=cosacosb-sinasinb⇒cos120°=032-112 ∵cos90°=0,sin90°=1,cos30°=32,sin30°=12⇒cos120°=-12Hence, the value of cos120° is -12.

How to find the value of $\cos (120 °)$ ? Solve with steps.