Question

evaluate cos(-135°)

Explanation:

Step1: Use the property of cosine function

$\cos(-\theta)=\cos\theta$, so $\cos(-135^{\circ})=\cos135^{\circ}$.

Step2: Rewrite the angle

$135^{\circ}=180^{\circ} - 45^{\circ}$, then $\cos135^{\circ}=\cos(180^{\circ}-45^{\circ})$.

Step3: Use the cosine subtraction formula

$\cos(A - B)=\cos A\cos B+\sin A\sin B$. Here $A = 180^{\circ}$, $B=45^{\circ}$. $\cos180^{\circ}=- 1$, $\sin180^{\circ}=0$, $\cos45^{\circ}=\frac{\sqrt{2}}{2}$, $\sin45^{\circ}=\frac{\sqrt{2}}{2}$.

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Answer:

$-\frac{\sqrt{2}}{2}$