cos⁡(−120o)=()\cos (-120^{o})=()
A. 12 \dfrac {1}{2}
B. −12- \dfrac {1}{2}
C. 32 \dfrac { \sqrt {3}}{2}
D. −32- \dfrac { \sqrt {3}}{2}

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Worked solution

1. 利用余弦函数的奇偶性化简负角

根据诱导公式 cos⁡(−θ)=cos⁡θ\cos(-\theta) = \cos\theta,可得:
cos⁡(−120∘)=cos⁡(120∘)\cos(-120^{\circ}) = \cos(120^{\circ})

2. 利用诱导公式将钝角转化为锐角

根据诱导公式 cos⁡(180∘−θ)=−cos⁡θ\cos(180^{\circ} - \theta) = -\cos\theta,可得:
cos⁡(120∘)=cos⁡(180∘−60∘)=−cos⁡(60∘)\cos(120^{\circ}) = \cos(180^{\circ} - 60^{\circ}) = -\cos(60^{\circ})

3. 代入特殊角三角函数值求出最终结果

因为 cos⁡(60∘)=12\cos(60^{\circ}) = \dfrac{1}{2},所以:
−cos⁡(60∘)=−12-\cos(60^{\circ}) = -\dfrac{1}{2}
因此,cos⁡(−120∘)=−12\cos(-120^{\circ}) = -\dfrac{1}{2}。
故选:B。

Answer

B

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