Get the solution to "Find the value of cos 225∘" - Plainmath

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mooltattawsmq8

Answered question

2022-12-28

Find the value of cos

225^{\circ}

Answer & Explanation

eyrurin3wj

Beginner2022-12-29Added 10 answers

Determining the worth of

\cos 225^{\circ}

\cos 225^{\circ}

can be expressed as

\cos 225^{\circ} = \cos (180^{\circ} + 45^{\circ})

\Rightarrow

\cos (180^{\circ} + 45^{\circ}) = \cos 180^{\circ} \times \cos 45^{\circ} - \sin 180^{\circ} \times \sin 45^{\circ}

;

[\cos (A + B) = \cos (A) \times \cos (B) - \sin (A) \times \sin (B)]

When we substitute the above angles' values, we obtain,

\cos 180^{\circ} = - 1, \cos 45^{\circ} = \frac{2}{2}, \sin 180^{\circ} = 0 and \sin 45^{\circ} = \frac{2}{2}

\cos (180^{\circ} + 45^{\circ}) = - 1 \times (\frac{2}{2}) - 0 \times (\frac{2}{2}) = - \frac{2}{2} = - \frac{1}{2}

Thus the value of

\cos 225^{\circ}

is

- \frac{1}{2}

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