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why does the moon have phases - Richter Guitar

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The diagonal of the rectangle is the diameter of the circle. Using the Pythagorean theorem, the diagonal \(d\) is:

📌 d = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm}

📌 The radius \(r\) of the circle is half of the diameter:

📌 r = \frac{5}{2} = 2.5 \text{ cm}

📌 C = 2\pi r = 2\pi \times 2.5 = 5\pi \text{ cm}

📌 Thus, the circumference of the circle is \(\boxed{5\pi}\) cm.

📌 Compute \(\tan 45^\circ\) using the unit circle and confirm its geometric interpretation.

📌 On the unit circle, the angle \(45^\circ\) corresponds to the point \(\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)\). The tangent of an angle is the ratio of the y-coordinate to the x-coordinate:

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