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52 lines
2.3 KiB
HTML
52 lines
2.3 KiB
HTML
<div class="book-prose">
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<h2 id="history" class="book-prose__heading">History</h2>
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<p>
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Advanced trigonometric methods were developed for astronomy, navigation, and surveying. Sine and
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cosine rule tables were essential long before modern calculators.
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</p>
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<h2 id="checkpoints" class="book-prose__heading">Checkpoints</h2>
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<details class="book-question">
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<summary class="book-question__prompt">Convert \(150^\circ\) to radians.</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(\frac{5\pi}{6}\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Find arc length for \(r=8\), \(\theta=\frac{\pi}{3}\).</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(s=r\theta=\frac{8\pi}{3}\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">In triangle, \(a=10,b=7,C=60^\circ\). Find \(c\).</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(c^2=10^2+7^2-2(10)(7)\cos60^\circ=79\), so \(c=\sqrt{79}\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Solve \(2\sin x=1\) for \(0^\circ\le x<360^\circ\).</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> \(x=30^\circ,150^\circ\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">For \(y=3\cos(2x)-1\), state amplitude and period.</summary>
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<div class="book-question__solution">
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<p><strong>Answer:</strong> Amplitude \(3\), period \(\pi\) radians (or \(180^\circ\)).</p>
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</div>
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</details>
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<h2 id="applications" class="book-prose__heading">Applications</h2>
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<ul>
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<li><strong>Wave modeling:</strong> sound, light, and AC signals.</li>
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<li><strong>Navigation:</strong> triangulation in maps and GPS support calculations.</li>
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<li><strong>Engineering:</strong> periodic motion and oscillation analysis.</li>
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</ul>
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<h2 id="references" class="book-prose__heading">References</h2>
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<ul>
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<li>Standard high-school advanced trigonometry syllabi (IB, A-Level, DSE extension).</li>
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<li>Precalculus texts on trig identities, equations, and graphs.</li>
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</ul>
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</div>
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