Question

current attempt in progress
compute cos225° exactly.
-\frac{\sqrt{3}}{2}
-\frac{\sqrt{2}}{2}
-\frac{1}{2}
\frac{1}{2}
\frac{\sqrt{2}}{2}
\frac{\sqrt{3}}{2}

Explanation:

Step1: Express \(225^{\circ}\) as sum of angles

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

Step2: Use the cosine addition formula \(\cos(A + B)=\cos A\cos B-\sin A\sin B\)

Here \(A = 180^{\circ}\), \(B=45^{\circ}\)
\(\cos(180^{\circ}+45^{\circ})=\cos180^{\circ}\cos45^{\circ}-\sin180^{\circ}\sin45^{\circ}\)

Step3: Substitute the values of trigonometric functions

We know that \(\cos180^{\circ}=- 1\), \(\sin180^{\circ}=0\), \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\)

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Answer:

\(-\frac{\sqrt{2}}{2}\) (the second option)