📐 TRIGONOMETRIC FORMULA SET
(For Class 10 Students – Quick Revision)
1️⃣ Basic Trigonometric Ratios
For an angle θ in a right-angled triangle:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cosec θ = 1 / sin θ
sec θ = 1 / cos θ
cot θ = 1 / tan θ
2️⃣ Reciprocal Relations
sin θ = 1 / cosec θ
cos θ = 1 / sec θ
tan θ = 1 / cot θ
3️⃣ Quotient Relations
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
4️⃣ Pythagorean Identities
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
5️⃣ Values of Trigonometric Ratios
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
| cosec θ | ∞ | 2 | √2 | 2/√3 | 1 |
| sec θ | 1 | 2/√3 | √2 | 2 | ∞ |
| cot θ | ∞ | √3 | 1 | 1/√3 | 0 |
6️⃣ Complementary Angle Identities
sin (90° − θ) = cos θ
cos (90° − θ) = sin θ
tan (90° − θ) = cot θ
sec (90° − θ) = cosec θ
cosec (90° − θ) = sec θ
7️⃣ Useful Tips for Exams
- Always convert division into multiplication using reciprocals
- Use identities to reduce expressions
- Memorize standard angle values
- Avoid calculation mistakes by simplifying step-by-step
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