[tex]3 \tan^{2} 4x - 1 = 0 \\ 0 \leqslant x = 2\pi[/tex]
TrigonomEtri
fungsi Tan
Penjelasan dengan langkah-langkah:
3 tan² 4x - 1= 0
[tex]\sf (\sqrt3 \tan 4x - 1)(\sqrt3 \tan 4x + 1) = 0[/tex]
[tex]\sf (\sqrt3 \tan 4x - 1)= 0 \ atau \ (\sqrt3 \tan 4x + 1) = 0[/tex]
√3 tan 4x = 1 atau √3 tan 4x = - 1
[tex]\sf \tan 4x = \frac{1}{\sqrt3}\ atau \tan 4x = -\frac{1}{\sqrt3}[/tex]
[tex]\sf \tan 4x = \tan \frac{\pi}{6} \ atau \ \tan 4x = \tan\ (-\frac{\pi}{6})[/tex]
i) tan 4x = tan π/6
4x = π/6 + k. π
x= ¹/₂₄ π + k .¹/₄ π
k = 0, x= ¹/₂₄ π
k = 1, x = ⁷/₂₄ π
k = 2, x = ¹³/₂₄ π
k = 3, x = ¹⁹/₂₄ π
k = 4, x = ²⁵/₂₄ π
k = 5, x = ³¹/₂₄ π
k = 6, x = ³⁷/₂₄ π
k = 7, x= ⁴³/₂₄ π
ii) tan 4x = tan (-π/6)
4x = -π/6 + k. π
x= -¹/₂₄ π + k .¹/₄ π
k = 0, x= - ¹/₂₄ π
k = 1, x = ⁵/₂₄ π
k = 2, x = ¹¹/₂₄ π
k = 3, x = ¹⁷/₂₄ π
k = 4, x = ²³/₂₄ π
k = 5, x = ²⁹/₂₄ π
k = 6, x = ³⁵/₂₄ π
k = 7, x= ⁴¹/₂₄ π
k= 8 , x = ⁴⁷/₂₄ π
HP x untuk 0 ≤ x ≤ 2π
x = ¹/₂₄ π , ⁵/₂₄ π, ⁷/₂₄ π, ¹¹/₂₄ π, ¹³/₂₄ π,
, ¹⁷/₂₄ π, ¹⁹/₂₄ π, ²³/₂₄ π, ²⁵/₂₄ π,²⁹/₂₄ π, ³¹/₂₄ π, ³⁵/₂₄ π
, ³⁷/₂₄ π, ⁴¹/₂₄ π, ⁴⁷/₂₄ π
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