How to simplify cos(pi - theta)?

Everett Douglas

Everett Douglas

Answered question

2023-01-02

How to simplify cos(πθ)?

Answer & Explanation

feod4rs

feod4rs

Beginner2023-01-03Added 6 answers

Triangle unit circle results in:
cos (pi - t) = -cos t
Goldwaagefhu

Goldwaagefhu

Beginner2023-01-04Added 2 answers

The unit circle is mentioned in a different answer, but using the identity is another way to reach the solution.
cos(α+β)=cos(α)cos(β)sin(α)sin(β)
along with the fact that cos(α)=cos(α)
With that, we have
cos(πθ)=cos(π+(θ))
=cos(π)cos(θ)sin(π)sin(θ)
=(1)cos(θ)0sin(θ)
=cos(θ)0
=cos(θ)
=cos(θ)

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