Trigonometriya jadvali
To'g'ri burchakli uchburchakda sinus — qarshi katetning gipotenuzaga nisbati, kosinus — yondosh katetning gipotenuzaga nisbati, tangens — qarshi katetning yondoshga nisbati.
Jadvaldagi 30°, 45°, 60° qiymatlarini yod bilish SHART: DTM va Milliy sertifikat topshiriqlarining ko'pchiligi aynan shu burchaklar bilan tuziladi. 30° va 60° teng tomonli uchburchakning yarmidan, 45° esa kvadrat diagonalidan chiqadi.
Formulalar
- Asosiy ayniyat
sin²α + cos²α = 1 - Tangens va kotangens
tg α = sin α / cos α, ctg α = cos α / sin α - Tangens–kotangens
tg α · ctg α = 1 - Qo'sh burchak
sin 2α = 2 sin α cos α, cos 2α = cos²α − sin²α - Yig'indi sinusi
sin(α ± β) = sin α cos β ± cos α sin β - Yig'indi kosinusi
cos(α ± β) = cos α cos β ∓ sin α sin β - Keltirish
sin(90° − α) = cos α, cos(90° − α) = sin α - Darajani pasaytirish
sin²α = (1 − cos 2α)/2, cos²α = (1 + cos 2α)/2
Asosiy burchaklar
| Burchak | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | √2/2 | √3/2 | 1 |
| cos | 1 | √3/2 | √2/2 | 1/2 | 0 |
| tg | 0 | √3/3 | 1 | √3 | — |
| ctg | — | √3 | 1 | √3/3 | 0 |
| radian | 0 | π/6 | π/4 | π/3 | π/2 |
90° dan keyin
| Burchak | 120° | 135° | 150° | 180° | 270° | 360° |
|---|---|---|---|---|---|---|
| sin | √3/2 | √2/2 | 1/2 | 0 | −1 | 0 |
| cos | −1/2 | −√2/2 | −√3/2 | −1 | 0 | 1 |
| tg | −√3 | −1 | −√3/3 | 0 | — | 0 |
| radian | 2π/3 | 3π/4 | 5π/6 | π | 3π/2 | 2π |
Savol va javob
sin 30° nechaga teng?
1/2 = 0,5
cos 60° nechaga teng?
1/2 = 0,5
tg 45° nechaga teng?
1 ga: 45° da ikki katet teng.
tg 90° nega aniqlanmagan?
tg α = sin α / cos α, cos 90° = 0 — nolga bo'lish mumkin emas.