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70 lines
2.1 KiB
HTML
70 lines
2.1 KiB
HTML
<div class="book-prose">
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<p>
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Advanced trigonometry extends right-triangle work to non-right triangles, radians, and trig
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graphs used in periodic modeling.
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</p>
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<h2 id="radian-measure" class="book-prose__heading">Radians and arc length</h2>
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<p>
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Convert degrees/radians:
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</p>
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<p class="book-formula">\[
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180^\circ=\pi\ \text{rad}.
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\]</p>
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<p>
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Arc length and sector area:
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</p>
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<p class="book-formula">\[
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s=r\theta,\qquad A=\frac12r^2\theta
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\]</p>
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<p>with \(\theta\) in radians.</p>
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<h2 id="sine-cosine-rules" class="book-prose__heading">Sine and cosine rules</h2>
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<p class="book-formula">\[
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\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}
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\]</p>
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<p class="book-formula">\[
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c^2=a^2+b^2-2ab\cos C.
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\]</p>
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<p>
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Use sine rule for side-angle opposite pairs; cosine rule for SAS or SSS cases.
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</p>
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<h2 id="area-triangle" class="book-prose__heading">Triangle area formula</h2>
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<p class="book-formula">\[
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\text{Area}=\frac12ab\sin C.
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\]</p>
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<p>
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Useful when two sides and included angle are known.
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</p>
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<h2 id="identities" class="book-prose__heading">Core identities</h2>
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<p class="book-formula">\[
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\sin^2x+\cos^2x=1,\qquad
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\tan x=\frac{\sin x}{\cos x}.
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\]</p>
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<h2 id="trig-equations" class="book-prose__heading">Solving basic trig equations</h2>
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<p>
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Solve in interval (e.g., \(0^\circ\le x<360^\circ\)) using unit-circle symmetry.
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</p>
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<p><strong>Example:</strong> \(\sin x=\frac12\Rightarrow x=30^\circ,150^\circ\).</p>
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<h2 id="graphs" class="book-prose__heading">Trigonometric graphs</h2>
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<p>
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For \(y=a\sin(bx)+d\) (similarly cosine):
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</p>
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<ul>
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<li>Amplitude \(=|a|\)</li>
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<li>Period \(=\frac{2\pi}{|b|}\) (or \(\frac{360^\circ}{|b|}\) in degrees mode)</li>
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<li>Vertical shift \(=d\)</li>
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</ul>
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<h2 id="exam-strategy" class="book-prose__heading">Exam strategy</h2>
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<ul>
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<li>Check calculator mode (degree/radian) before solving.</li>
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<li>State interval when listing trig equation solutions.</li>
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<li>Draw quick triangle sketch for sine/cosine rule setup.</li>
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<li>Keep exact radian forms when possible.</li>
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</ul>
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</div>
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