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Question

Why are cosπ and cos-π both equal to -1?


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Solution

Determine the value of cosπ and cos-π.

We know that cosπ=cos180° and cos0=1.

Also, cos180° lies in the second quadrant where the cosine function is negative.

cos180°=cos180+0cos180°=-cos0cos180°=-1

By using the trigonometry identity, cosθ=cos-θ.

Thus, cosπ=cos-π=-1.

Hence, using the identity cosθ=cos-θ, the value of cosπ and cos-π are equal to -1.


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