Would anyone be willing to provide and explain a geometric

Jayla Christensen

Jayla Christensen

Answered question

2022-06-14

Would anyone be willing to provide and explain a geometric proof that there is an angle θ such that cos ( θ ) = θ

Answer & Explanation

Dustin Durham

Dustin Durham

Beginner2022-06-15Added 31 answers

Consider the function f ( θ ) = cos θ θ
Then f is clearly continuous, and f(0)=1>0 while f(5)<0. By the intermediate value theorem, there is a point in the middle where f(θ)=0. At that point we necessarily have cos θ = θ

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