TRIGONOMETRY
Basic Trigonometric Ratios
For a right-angled triangle:
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sin θ = Perpendicular / Hypotenuse
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cos θ = Base / Hypotenuse
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tan θ = Perpendicular / Base
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cot θ = 1/tan θ = Base / Perpendicular
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sec θ = 1/cos θ = Hypotenuse / Base
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cosec θ = 1/sin θ = Hypotenuse / Perpendicular
Trigonometric Ratios of Standard Angles
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sinθ | 0 | 1/2 | √2/2 | √3/2 | 1 |
| cosθ | 1 | √3/2 | √2/2 | 1/2 | 0 |
| tanθ | 0 | 1/√3 | 1 | √3 | Not Defined |
| cotθ | Not Defined | √3 | 1 | 1/√3 | 0 |
| secθ | 1 | 2/√3 | √2 | 2 | Not Defined |
| cosecθ | Not Defined | 2 | √2 | 2/√3 | 1 |
Relations Between Trigonometric Ratios
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sin²θ + cos²θ = 1
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1 + tan²θ = sec²θ
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1 + cot²θ = cosec²θ
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tanθ = sinθ / cosθ
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cotθ = cosθ /
Complementary Angle Identities
(θ + (90° − θ) = 90°)
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sin (90° − θ) = cos θ
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cos (90° − θ) = sin θ
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tan (90° − θ) = cot θ
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cot (90° − θ) = tan θ
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sec (90° − θ) = cosec θ
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cosec (90° − θ) = sec θ
Height & Distance Formulas (Basic)
Uses tan θ = Perpendicular / Base
Applications:
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Height of tower = Base × tanθ
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Distance of object = Height / tanθ
