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Fungsi \( \quad f(x)=\sin \left(x-60^{0}\right) \) untuk \( 0^{0} \leq \mathrm{x} \leq 360^{0} \), naik pada interval... A. \( 0^{0} \leq \mathrm{x}<150^{0} \) B. \( 0^{0}<\mathrm{x}<330^{0} \) C. \( 90^{0}<\mathrm{x}<180^{0} \) D. \( 0^{0} \leq \mathrm{x}<150^{0} \) atau \( 330^{\circ}<\mathrm{x} \leq 360^{\circ} \) E. \( 0^{0} \leq \mathrm{x}<90^{\circ} \) atau \( 330^{\circ}<\mathrm{x} \leq 360^{\circ} \)

Ask by Reyes Gray. in Indonesia
Mar 14,2025

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Fungsi \( f(x) = \sin(x - 60^{\circ}) \) naik pada interval \( 0^{\circ} \leq x < 150^{\circ} \) atau \( 330^{\circ} < x \leq 360^{\circ} \).

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The Deep Dive

Fungsi \( f(x) = \sin(x - 60^\circ) \) merupakan fungsi sinus yang mengalami pergeseran \( 60^\circ \) ke kanan pada sumbu \( x \). Fungsi sinus naik ketika sudutnya berada antara \( 0^\circ \) hingga \( 180^\circ \). Oleh karena itu, perlu dicocokkan interval tersebut setelah mengalikan dengan pergeseran \( 60^\circ \). Dengan cara ini, kita dapat menemukan interval di mana \( f(x) \) naik. Dengan menghitung, kita tahu bahwa \( f(x) \) akan naik pada: 1. \( (60^\circ, 240^\circ) \) sebelum mengaplikasikan batasan \( 0^\circ \leq x \leq 360^\circ \). 2. Setelah memperhatikan batasan, kita dapat menemukan bahwa \( f(x) \) naik dari \( 60^\circ \) hingga \( 150^\circ \) dan dari \( 330^\circ \) hingga \( 360^\circ \). Jadi, interval di mana fungsi \( f(x) \) naik adalah: **(D) \( 0^\circ \leq x < 150^\circ \) atau \( 330^\circ < x \leq 360^\circ \)**.

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