Pertanyaan

Tentukan nilai x yang memenuhi persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ . a. ( sin 3 x − cos 4 x ) ( cos 5 x − sin 4 x ) = 0

Tentukan nilai $x$ yang memenuhi persamaan berikut untuk $0^{\circ} \leq x \leq 36 0^{\circ}$ .

a. $(sin 3 x - cos 4 x) (cos 5 x - sin 4 x) = 0$

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S. Nur

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Jawaban terverifikasi

Jawaban

nilai x yang memenuhi persamaan ( sin 3 x − cos 4 x ) ( cos 5 x − sin 4 x ) = 0 untuk 0 ∘ ≤ x ≤ 36 0 ∘ adalah { 12 , 9 ∘ ; 3 0 ∘ ; 6 4 ∘ ; 7 0 ∘ ; 11 0 ∘ ; 115 , 5 ; 15 0 ∘ ; 166 , 6 ∘ ; 19 0 ∘ ; 218 , 1 ∘ ; 23 0 ∘ ; 269 , 2 ∘ ; 27 0 ∘ ; 31 0 ∘ ; 320 , 7 ∘ } .

nilai

x

yang memenuhi persamaan

(sin 3 x - cos 4 x) (cos 5 x - sin 4 x) = 0

untuk

0^{\circ} \leq x \leq 36 0^{\circ}

adalah

{12, 9^{\circ}; 3 0^{\circ}; 6 4^{\circ}; 7 0^{\circ}; 11 0^{\circ}; 115, 5; 15 0^{\circ}; 166, 6^{\circ}; 19 0^{\circ}; 218, 1^{\circ}; 23 0^{\circ}; 269, 2^{\circ}; 27 0^{\circ}; 31 0^{\circ}; 320, 7^{\circ}}

Pembahasan

Ingat kembali: cos ( 9 0 ∘ − A ) = sin A cos A − cos B = − 2 ⋅ sin 2 1 ( A + B ) ⋅ sin 2 1 ( A − B ) sin x = sin α { x = α + k ⋅ 36 0 ∘ x = ( 18 0 ∘ − α ) + k ⋅ 36 0 ∘ Diberikan persamaan ( sin 3 x − cos 4 x ) ( cos 5 x − sin 4 x ) = 0 untuk 0 ∘ ≤ x ≤ 36 0 ∘ . Maka: - Untuk ( sin 3 x − cos 4 x ) = 0 ( sin 3 x − cos 4 x ) sin 3 x − cos 4 x cos ( 9 0 ∘ − 3 x ) − cos 4 x − 2 ⋅ sin 2 1 ( 9 0 ∘ + x ) ⋅ sin 2 1 ( 9 0 ∘ − 7 x ) sin 2 1 ( 9 0 ∘ + x ) ⋅ sin 2 1 ( 9 0 ∘ − 7 x ) = = = = = 0 0 0 0 0 Bentuk sin 2 1 ( 9 0 ∘ + x ) = 0 sin 2 1 ( 9 0 ∘ + x ) = 0 sin 2 1 ( 9 0 ∘ + x ) = sin 0 ∘ Persamaan sinus (1) 2 1 ( 9 0 ∘ + x ) 9 0 ∘ + x x = = = 0 ∘ + k ⋅ 36 0 ∘ 0 ∘ + k ⋅ 72 0 ∘ − 9 0 ∘ + k ⋅ 72 0 ∘ ( tidak memenuhi ) Persamaan sinus (2) 2 1 ( 9 0 ∘ + x ) 2 1 ( 9 0 ∘ + x ) 9 0 ∘ + x x = = = = ( 18 0 ∘ − 0 ∘ ) + k ⋅ 36 0 ∘ 18 0 ∘ + k ⋅ 36 0 ∘ 36 0 ∘ + k ⋅ 72 0 ∘ 27 0 ∘ + k ⋅ 72 0 ∘ Bentuk sin 2 1 ( 9 0 ∘ − 7 x ) = 0 sin 2 1 ( 9 0 ∘ − 7 x ) = 0 sin 2 1 ( 9 0 ∘ − 7 x ) = sin 0 ∘ Persamaan sinus (1) 2 1 ( 9 0 ∘ − 7 x ) 9 0 ∘ − 7 x − 7 x x = = = = 0 ∘ + k ⋅ 36 0 ∘ 0 ∘ + k ⋅ 72 0 ∘ − 9 0 ∘ + k ⋅ 72 0 ∘ 12 , 9 − k ⋅ 102 , 6 ∘ Persamaan sinus (2) 2 1 ( 9 0 ∘ − 7 x ) 2 1 ( 9 0 ∘ − 7 x ) 9 0 ∘ − 7 x − 7 x x = = = = = ( 18 0 ∘ − 0 ∘ ) + k ⋅ 36 0 ∘ 180 0 ∘ + k ⋅ 36 0 ∘ 36 0 ∘ + k ⋅ 72 0 ∘ 27 0 ∘ + k ⋅ 72 0 ∘ − 38 , 6 − k ⋅ 102 , 6 ∘ - Untuk ( cos 5 x − sin 4 x ) = 0 ( cos 5 x − sin 4 x ) cos 5 x − sin 4 x cos 5 x − cos ( 9 0 ∘ − 4 x ) − 2 ⋅ sin 2 1 ( x + 9 0 ∘ ) ⋅ sin 2 1 ( 9 x + 9 0 ∘ ) sin 2 1 ( x + 9 0 ∘ ) ⋅ sin 2 1 ( 9 x + 9 0 ∘ ) = = = = = 0 0 0 0 0 Bentuk sin 2 1 ( x + 9 0 ∘ ) = 0 sin 2 1 ( x + 9 0 ∘ ) = 0 sin 2 1 ( x + 9 0 ∘ ) = sin 0 ∘ Persamaan sinus (1) 2 1 ( x + 9 0 ∘ ) x + 9 0 ∘ x = = = 0 ∘ + k ⋅ 36 0 ∘ 0 ∘ + k ⋅ 72 0 ∘ − 9 0 ∘ + k ⋅ 720 ( tidak memenuhi ) Persamaan sinus (2) 2 1 ( x + 9 0 ∘ ) 2 1 ( x + 9 0 ∘ ) x + 9 0 ∘ x = = = = ( 18 0 ∘ − 0 ∘ ) + k ⋅ 36 0 ∘ 18 0 ∘ + k ⋅ 36 0 ∘ 36 0 ∘ + k ⋅ 72 0 ∘ 27 0 ∘ + k ⋅ 36 0 ∘ Bentuk sin 2 1 ( 9 x + 9 0 ∘ ) = 0 sin 2 1 ( 9 x + 9 0 ∘ ) = 0 sin 2 1 ( 9 x + 9 0 ∘ ) = sin 0 ∘ Persamaan sinus (1) 2 1 ( 9 x + 9 0 ∘ ) 9 x + 9 0 ∘ 9 x x = = = = 0 ∘ + k ⋅ 36 0 ∘ 0 ∘ + k ⋅ 72 0 ∘ − 9 0 ∘ + k ⋅ 72 0 ∘ − 1 0 ∘ + k ⋅ 8 0 ∘ Persamaan sinus (2) 2 1 ( 9 x + 9 0 ∘ ) 2 1 ( 9 x + 9 0 ∘ ) 9 x + 9 0 ∘ 9 x x = = = = = ( 18 0 ∘ − 0 ∘ ) + k ⋅ 36 0 ∘ 18 0 ∘ + k ⋅ 36 0 ∘ 36 0 ∘ + k ⋅ 72 0 ∘ 27 0 ∘ + k ⋅ 72 0 ∘ 3 0 ∘ + k ⋅ 8 0 ∘ Jadi,nilai x yang memenuhi persamaan ( sin 3 x − cos 4 x ) ( cos 5 x − sin 4 x ) = 0 untuk 0 ∘ ≤ x ≤ 36 0 ∘ adalah { 12 , 9 ∘ ; 3 0 ∘ ; 6 4 ∘ ; 7 0 ∘ ; 11 0 ∘ ; 115 , 5 ; 15 0 ∘ ; 166 , 6 ∘ ; 19 0 ∘ ; 218 , 1 ∘ ; 23 0 ∘ ; 269 , 2 ∘ ; 27 0 ∘ ; 31 0 ∘ ; 320 , 7 ∘ } .

Ingat kembali:

$cos (9 0^{\circ} - A) = sin A$
$cos A - cos B = - 2 \cdot sin \frac{1}{2} (A + B) \cdot sin \frac{1}{2} (A - B)$
$sin x = sin α {x = α + k \cdot 36 0^{\circ} x = (18 0^{\circ} - α) + k \cdot 36 0^{\circ}$

Diberikan persamaan $(sin 3 x - cos 4 x) (cos 5 x - sin 4 x) = 0$ untuk $0^{\circ} \leq x \leq 36 0^{\circ}$ . Maka:

- Untuk $(sin 3 x - cos 4 x) = 0$

$(sin 3 x - cos 4 x) sin 3 x - cos 4 x cos (9 0^{\circ} - 3 x) - cos 4 x - 2 \cdot sin \frac{1}{2} (9 0^{\circ} + x) \cdot sin \frac{1}{2} (9 0^{\circ} - 7 x) sin \frac{1}{2} (9 0^{\circ} + x) \cdot sin \frac{1}{2} (9 0^{\circ} - 7 x) = = = = = 00000$

Bentuk $sin \frac{1}{2} (9 0^{\circ} + x) = 0$

$sin \frac{1}{2} (9 0^{\circ} + x) = 0 sin \frac{1}{2} (9 0^{\circ} + x) = sin 0^{\circ}$

Persamaan sinus (1)

$\frac{1}{2} (9 0^{\circ} + x) 9 0^{\circ} + x x = = = 0^{\circ} + k \cdot 36 0^{\circ} 0^{\circ} + k \cdot 72 0^{\circ} - 9 0^{\circ} + k \cdot 72 0^{\circ} (tidak memenuhi)$

Persamaan sinus (2)

$\frac{1}{2} (9 0^{\circ} + x) \frac{1}{2} (9 0^{\circ} + x) 9 0^{\circ} + x x = = = = (18 0^{\circ} - 0^{\circ}) + k \cdot 36 0^{\circ} 18 0^{\circ} + k \cdot 36 0^{\circ} 36 0^{\circ} + k \cdot 72 0^{\circ} 27 0^{\circ} + k \cdot 72 0^{\circ}$

$\boldsymbol k\boldsymbol=\mathbf0\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{270}\boldsymbol\textdegree\boldsymbol+\mathbf0\boldsymbol\cdot\mathbf{720}\boldsymbol\textdegree\boldsymbol=\mathbf{270}\boldsymbol\textdegree\boldsymbol+\mathbf0\boldsymbol\textdegree\boldsymbol=\mathbf{270}\boldsymbol\textdegree$

Bentuk $sin \frac{1}{2} (9 0^{\circ} - 7 x) = 0$

$sin \frac{1}{2} (9 0^{\circ} - 7 x) = 0 sin \frac{1}{2} (9 0^{\circ} - 7 x) = sin 0^{\circ}$

Persamaan sinus (1)

$\frac{1}{2} (9 0^{\circ} - 7 x) 9 0^{\circ} - 7 x - 7 x x = = = = 0^{\circ} + k \cdot 36 0^{\circ} 0^{\circ} + k \cdot 72 0^{\circ} - 9 0^{\circ} + k \cdot 72 0^{\circ} 12, 9 - k \cdot 102, 6^{\circ}$

$\style{font-size:12px}{\boldsymbol k\boldsymbol=\mathbf0\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol-\mathbf0\boldsymbol\cdot\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol\textdegree\boldsymbol-\mathbf0\boldsymbol\textdegree\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\boldsymbol-\mathbf1\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol-{\boldsymbol(\boldsymbol-\mathbf1\boldsymbol)}\boldsymbol\cdot\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol\textdegree\boldsymbol+\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\mathbf{115}\boldsymbol,\mathbf5\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\boldsymbol-\mathbf2\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol-{\boldsymbol(\boldsymbol-\mathbf2\boldsymbol)}\boldsymbol\cdot\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol\textdegree\boldsymbol+\mathbf{205}\boldsymbol,\mathbf2\boldsymbol\textdegree\boldsymbol=\mathbf{218}\boldsymbol,\mathbf1\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\boldsymbol-\mathbf3\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol-{\boldsymbol(\boldsymbol-\mathbf3\boldsymbol)}\boldsymbol\cdot\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\mathbf{12}\boldsymbol,\mathbf9\boldsymbol\textdegree\boldsymbol+\mathbf{307}\boldsymbol,\mathbf8\boldsymbol\textdegree\boldsymbol=\mathbf{320}\boldsymbol,\mathbf7\boldsymbol\textdegree}$

Persamaan sinus (2)

$\frac{1}{2} (9 0^{\circ} - 7 x) \frac{1}{2} (9 0^{\circ} - 7 x) 9 0^{\circ} - 7 x - 7 x x = = = = = (18 0^{\circ} - 0^{\circ}) + k \cdot 36 0^{\circ} 180 0^{\circ} + k \cdot 36 0^{\circ} 36 0^{\circ} + k \cdot 72 0^{\circ} 27 0^{\circ} + k \cdot 72 0^{\circ} - 38, 6 - k \cdot 102, 6^{\circ}$

$\style{font-size:12px}{\boldsymbol k\boldsymbol=\boldsymbol-\mathbf1\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\boldsymbol-\mathbf{38}\boldsymbol,\mathbf6\boldsymbol-{\boldsymbol(\boldsymbol-\mathbf1\boldsymbol)}\boldsymbol\cdot\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\boldsymbol-\mathbf{38}\boldsymbol,\mathbf6\boldsymbol+\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\mathbf{64}\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\boldsymbol-\mathbf2\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\boldsymbol-\mathbf{38}\boldsymbol,\mathbf6\boldsymbol-{\boldsymbol(\boldsymbol-\mathbf2\boldsymbol)}\boldsymbol\cdot\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\boldsymbol-\mathbf{38}\boldsymbol,\mathbf6\boldsymbol+\mathbf{205}\boldsymbol,\mathbf2\boldsymbol\textdegree\boldsymbol=\mathbf{166}\boldsymbol,\mathbf6\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\boldsymbol-\mathbf3\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\boldsymbol-\mathbf{38}\boldsymbol,\mathbf6\boldsymbol-{\boldsymbol(\boldsymbol-\mathbf3\boldsymbol)}\boldsymbol\cdot\mathbf{102}\boldsymbol,\mathbf6\boldsymbol\textdegree\boldsymbol=\boldsymbol-\mathbf{38}\boldsymbol,\mathbf6\boldsymbol+\mathbf{307}\boldsymbol,\mathbf8\boldsymbol\textdegree\boldsymbol=\mathbf{269}\boldsymbol,\mathbf2\boldsymbol\textdegree}$

- Untuk $(cos 5 x - sin 4 x) = 0$

$(cos 5 x - sin 4 x) cos 5 x - sin 4 x cos 5 x - cos (9 0^{\circ} - 4 x) - 2 \cdot sin \frac{1}{2} (x + 9 0^{\circ}) \cdot sin \frac{1}{2} (9 x + 9 0^{\circ}) sin \frac{1}{2} (x + 9 0^{\circ}) \cdot sin \frac{1}{2} (9 x + 9 0^{\circ}) = = = = = 00000$

Bentuk $sin \frac{1}{2} (x + 9 0^{\circ}) = 0$

$sin \frac{1}{2} (x + 9 0^{\circ}) = 0 sin \frac{1}{2} (x + 9 0^{\circ}) = sin 0^{\circ}$

Persamaan sinus (1)

$\frac{1}{2} (x + 9 0^{\circ}) x + 9 0^{\circ} x = = = 0^{\circ} + k \cdot 36 0^{\circ} 0^{\circ} + k \cdot 72 0^{\circ} - 9 0^{\circ} + k \cdot 720 (tidak memenuhi)$

Persamaan sinus (2)

$\frac{1}{2} (x + 9 0^{\circ}) \frac{1}{2} (x + 9 0^{\circ}) x + 9 0^{\circ} x = = = = (18 0^{\circ} - 0^{\circ}) + k \cdot 36 0^{\circ} 18 0^{\circ} + k \cdot 36 0^{\circ} 36 0^{\circ} + k \cdot 72 0^{\circ} 27 0^{\circ} + k \cdot 36 0^{\circ}$

$\boldsymbol k\boldsymbol=\mathbf0\boldsymbol\rightarrow\begin{array}{rcl}&&\boldsymbol x\end{array}\begin{array}{rcl}&\boldsymbol=&\end{array}\begin{array}{rcl}&&\mathbf{270}\end{array}\begin{array}{rcl}&&\boldsymbol\textdegree\end{array}\begin{array}{rcl}&&\boldsymbol+\end{array}\begin{array}{rcl}&&\boldsymbol k\end{array}\begin{array}{rcl}&&\boldsymbol\cdot\end{array}\begin{array}{rcl}&&\mathbf{360}\end{array}\begin{array}{rcl}&&\boldsymbol\textdegree\end{array}\begin{array}{rcl}&\boldsymbol=&\end{array}\begin{array}{rcl}&&\mathbf{270}\end{array}\begin{array}{rcl}&&\boldsymbol\textdegree\end{array}\begin{array}{rcl}&&\boldsymbol+\end{array}\begin{array}{rcl}&&\mathbf0\end{array}\begin{array}{rcl}&&\boldsymbol\textdegree\end{array}\begin{array}{rcl}&\boldsymbol=&\end{array}\begin{array}{rcl}&&\mathbf{270}\end{array}\begin{array}{rcl}&&\boldsymbol\textdegree\end{array}$

Bentuk $sin \frac{1}{2} (9 x + 9 0^{\circ}) = 0$

$sin \frac{1}{2} (9 x + 9 0^{\circ}) = 0 sin \frac{1}{2} (9 x + 9 0^{\circ}) = sin 0^{\circ}$

Persamaan sinus (1)

$\frac{1}{2} (9 x + 9 0^{\circ}) 9 x + 9 0^{\circ} 9 x x = = = = 0^{\circ} + k \cdot 36 0^{\circ} 0^{\circ} + k \cdot 72 0^{\circ} - 9 0^{\circ} + k \cdot 72 0^{\circ} - 1 0^{\circ} + k \cdot 8 0^{\circ}$

$\style{font-size:12px}{\boldsymbol k\boldsymbol=\mathbf1\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf1\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf{80}\boldsymbol\textdegree\boldsymbol=\mathbf{70}\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\mathbf2\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf2\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf{160}\boldsymbol\textdegree\boldsymbol=\mathbf{150}\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\mathbf3\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf3\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf{240}\boldsymbol\textdegree\boldsymbol=\mathbf{230}\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\mathbf4\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf4\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\boldsymbol-\mathbf{10}\boldsymbol\textdegree\boldsymbol+\mathbf{320}\boldsymbol\textdegree\boldsymbol=\mathbf{310}\boldsymbol\textdegree}$

Persamaan sinus (2)

$\frac{1}{2} (9 x + 9 0^{\circ}) \frac{1}{2} (9 x + 9 0^{\circ}) 9 x + 9 0^{\circ} 9 x x = = = = = (18 0^{\circ} - 0^{\circ}) + k \cdot 36 0^{\circ} 18 0^{\circ} + k \cdot 36 0^{\circ} 36 0^{\circ} + k \cdot 72 0^{\circ} 27 0^{\circ} + k \cdot 72 0^{\circ} 3 0^{\circ} + k \cdot 8 0^{\circ}$

$\style{font-size:12px}{\boldsymbol k\boldsymbol=\mathbf0\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf0\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf0\boldsymbol=\mathbf{30}\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\mathbf1\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf1\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf{80}\boldsymbol\textdegree\boldsymbol=\mathbf{110}\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\mathbf2\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf2\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf{160}\boldsymbol\textdegree\boldsymbol=\mathbf{190}\boldsymbol\textdegree\\\boldsymbol k\boldsymbol=\mathbf3\boldsymbol\rightarrow\boldsymbol x\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf3\boldsymbol\cdot\mathbf{80}\boldsymbol\textdegree\boldsymbol=\mathbf{30}\boldsymbol\textdegree\boldsymbol+\mathbf{240}\boldsymbol\textdegree\boldsymbol=\mathbf{270}\boldsymbol\textdegree}$

Jadi, nilai $x$ yang memenuhi persamaan $(sin 3 x - cos 4 x) (cos 5 x - sin 4 x) = 0$ untuk $0^{\circ} \leq x \leq 36 0^{\circ}$ adalah ${12, 9^{\circ}; 3 0^{\circ}; 6 4^{\circ}; 7 0^{\circ}; 11 0^{\circ}; 115, 5; 15 0^{\circ}; 166, 6^{\circ}; 19 0^{\circ}; 218, 1^{\circ}; 23 0^{\circ}; 269, 2^{\circ}; 27 0^{\circ}; 31 0^{\circ}; 320, 7^{\circ}}$ .