Pertanyaan

Nyatakan perbandingan trigonometri berikut ini dalam perbandingan trigonometri sudut komplemennya. a. sin 13 6 ∘ b. cos 10 5 ∘ c. d. sec 14 0 ∘ e. cos ec 11 6 ∘

Nyatakan perbandingan trigonometri berikut ini dalam perbandingan trigonometri sudut komplemennya.

a. $sin 13 6^{\circ}$
b. $cos 10 5^{\circ}$
c. $\style{font-size:14px}\cot\style{font-size:14px}\;\style{font-size:14px}{156}\style{font-size:14px}\textdegree$
d. $sec 14 0^{\circ}$
e. $cos ec 11 6^{\circ}$

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Jawaban terverifikasi

Jawaban

.

$\begin{array}{rcl}&&\mathrm a\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\sin\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&136\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&\sin\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&44\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm b\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\cos\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&105\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&-\end{array}\begin{array}{rcl}&&\cos\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&75\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm c\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\cot\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&156\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&-\end{array}\begin{array}{rcl}&&\cot\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&24\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm d\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\sec\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&140\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&-\end{array}\begin{array}{rcl}&&\sec\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&40\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm e\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm{cosec}\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&116\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&\end{array}\begin{array}{rcl}&&\mathrm{cosec}\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&64\end{array}\begin{array}{rcl}&&\textdegree\end{array}$ .

Pembahasan

Dengan menggunakan rumus trigonometri sudut berelasi pada kuadran II, maka: sin ( 180 − a ) ∘ cos ( 180 − a ) ∘ cosec ( 180 − a ) ∘ cot ( 180 − a ) ∘ sec ( 180 − a ) ∘ a . sin 13 6 ∘ b . cos 10 5 ∘ c . cot 15 6 ∘ d . sec 14 0 ∘ e . cosec 11 6 ∘ = = = = = = = = = = = = = = = sin a ∘ − cos a ∘ − sec a ∘ − cotan a ∘ sec a ∘ sin ( 180 − 44 ) ∘ sin 4 4 ∘ cos ( 180 − 75 ) ∘ − cos 7 5 ∘ cot ( 180 − 24 ) ∘ − cot 2 4 ∘ sec ( 180 − 40 ) ∘ − sec 4 0 ∘ cosec ( 180 − 64 ) ∘ cosec 6 4 ∘ Jadi, .

Dengan menggunakan rumus trigonometri sudut berelasi pada kuadran II, maka:

$sin (180 - a)^{\circ} cos (180 - a)^{\circ} cosec (180 - a)^{\circ} cot (180 - a)^{\circ} sec (180 - a)^{\circ} a . sin 13 6^{\circ} b . cos 10 5^{\circ} c . cot 15 6^{\circ} d . sec 14 0^{\circ} e . cosec 11 6^{\circ} = = = = = = = = = = = = = = = sin a^{\circ} - cos a^{\circ} - sec a^{\circ} - cotan a^{\circ} sec a^{\circ} sin (180 - 44)^{\circ} sin 4 4^{\circ} cos (180 - 75)^{\circ} - cos 7 5^{\circ} cot (180 - 24)^{\circ} - cot 2 4^{\circ} sec (180 - 40)^{\circ} - sec 4 0^{\circ} cosec (180 - 64)^{\circ} cosec 6 4^{\circ}$

Jadi, $\begin{array}{rcl}&&\mathrm a\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\sin\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&136\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&\sin\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&44\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm b\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\cos\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&105\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&-\end{array}\begin{array}{rcl}&&\cos\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&75\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm c\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\cot\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&156\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&-\end{array}\begin{array}{rcl}&&\cot\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&24\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm d\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\sec\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&140\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&-\end{array}\begin{array}{rcl}&&\sec\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&40\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&&,\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm e\end{array}\begin{array}{rcl}&&.\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&\mathrm{cosec}\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&116\end{array}\begin{array}{rcl}&&\textdegree\end{array}\begin{array}{rcl}&=&\end{array}\begin{array}{rcl}&&\end{array}\begin{array}{rcl}&&\mathrm{cosec}\end{array}\begin{array}{rcl}&&\;\end{array}\begin{array}{rcl}&&64\end{array}\begin{array}{rcl}&&\textdegree\end{array}$ .