Nilai dari cos 300° sin 120° - tan 135° cos 330° adalah [tex] \dfrac{3}{4} \sqrt{3} [/tex] .
PEMBAHASAN
Trigonometri
Perbandingan Sudut Berelasi
1. Kuadran I
(Semua bernilai +)
- sin (90° - α) = cos α
- cos (90° - α) = sin α
- tan (90° - α) = cot α
- cot (90° - α) = tan α
2. Kuadran II
(Sin bernilai +)
- sin (90° + α) = cos α
- cos (90° + α) = -sin α
- tan (90° + α) = -cot α
- cot (90° + α) = -tan α
- sin (180° - α) = sin α
- cos (180° - α) = -cos α
- tan (180° - α) = -tan α
- cot (180° - α) = -cot α
3. Kuadran III
(Tan bernilai +)
- sin (180° + α) = -sin α
- cos (180° + α) = -cos α
- tan (180° + α) = tan α
- cot (180° + α) = cot α
- sin (270° - α) = -cos α
- cos (270° - α) = -sin α
- tan (270° - α) = cot α
- cot (270° - α) = tan α
4. Kuadran IV
(Cos bernilai +)
- sin (270° + α) = -cos α
- cos (270° + α) = sin α
- tan (270° + α) = -cot α
- cot (270° - α) = -tan α
- sin (360° - α) = -sin α
- cos (360° - α) = cos α
- tan (360° - α) = -tan α
- cot (360° - α) = -cot α
DIKETAHUI:
cos 300° sin 120° - tan 135° cos 330°
DITANYA:
Nilai/hasil?
PENYELESAIAN:
[tex] \rm{ {cos \: 300}^{o} \: {sin \: 120}^{o} \: - \: {tan \: 135}^{o} \: {cos \: 330}^{o}} [/tex]
[tex] \rm{ {cos \: (360 - 60) }^{o} \: {sin \: (180 - 60) }^{o} \: - \: {tan \: (180 - 45)}^{o} \: cos \: {(360 - 30) }^{o} }[/tex]
[tex] \rm{cos \: {60}^{o} \: sin \: {60}^{o} \: - \: ( - tan \: {45}^{o} ) \: cos \: {30}^{o} }[/tex]
[tex] \dfrac{1}{2} \: \times \: \dfrac{1}{2} \sqrt{3} \: - \: ( - 1 \: \times \: \dfrac{1}{2} \sqrt{3} )[/tex]
[tex] \dfrac{1}{4} \sqrt{3} \: - \: ( - \dfrac{1}{2} \sqrt{3} )[/tex]
[tex] \dfrac{1}{4} \sqrt{3} \: + \: \dfrac{1}{2} \sqrt{3} [/tex]
[tex] \dfrac{1 \: + \: 2}{4} \sqrt{3} [/tex]
[tex] \boxed{\dfrac{3}{4} \sqrt{3}} [/tex]
KESIMPULAN:
Nilai dari cos 300° sin 120° - tan 135° cos 330° adalah [tex] \dfrac{3}{4} \sqrt{3} [/tex] .
PELAJARI LEBIH LANJUT
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DETAIL JAWABAN:
Kelas : 10
Mapel : Matematika
Bab : 7 - Trigonometri
Kode Kategorisasi : 10.2.7
Kata Kunci : perbandingan, sudut berelasi
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