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Home » First, express \( z(t) \) in terms of cosine and sine: - Deep Underground Poetry

First, express \( z(t) \) in terms of cosine and sine: - Deep Underground Poetry

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 The hypotenuse \( c = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \).

📌 The area \( A \) of the triangle is \( rac{1}{2} imes 8 imes 15 = 60 \).

📌 The semi-perimeter \( s = rac{8 + 15 + 17}{2} = 20 \).

📌 The radius \( r \) of the inscribed circle is given by \( r = rac{A}{s} = rac{60}{20} = 3 \).

📌 Solve for \( x \) in the equation \( \log_2(x+1) + \log_2(x-1) = 3 \).

📌 Combine logs: \( \log_2((x+1)(x-1)) = 3 \).

📌 So, \( (x+1)(x-1) = 2^3 = 8 \).

📌 Then \( x^2 - 1 = 8 \).

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