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10 cards from this deck
Use Rcos(θ±α)R \cos(\theta \pm \alpha)Rcos(θ±α) with R=a2+b2R = \sqrt{a^2 + b^2}R=a2+b2.
R=a2+b2R = \sqrt{a^2 + b^2}R=a2+b2, where aaa and bbb are coefficients.
α=tan−1(b/a)\alpha = \tan^{-1}(b/a)α=tan−1(b/a), relating to aaa and bbb coefficients.
Start with Rcos(θ−α)R \cos(\theta - \alpha)Rcos(θ−α) expansion.
Use Rsin(θ±α)R \sin(\theta \pm \alpha)Rsin(θ±α) with R=a2+b2R = \sqrt{a^2 + b^2}R=a2+b2.
R=32+42=25=5R = \sqrt{3^2 + 4^2} = \sqrt{25} = 5R=32+42=25=5.
R=5R = 5R=5, α=tan−1(4/3)\alpha = \tan^{-1}(4/3)α=tan−1(4/3), combine to get desired form.
θ=cos−1(2/5)+α\theta = \cos^{-1}(2/5) + \alphaθ=cos−1(2/5)+α or 360°−cos−1(2/5)+α360° - \cos^{-1}(2/5) + \alpha360°−cos−1(2/5)+α.
Simplifies analysis of oscillatory motion and waves.
Analyzes AC circuits with sinusoidal voltages and currents.
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