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Trigonometry Reference Guide
Six Trigonometric Functions
Primary Functions
- Sine (sin θ) = opposite / hypotenuse
- Cosine (cos θ) = adjacent / hypotenuse
- Tangent (tan θ) = opposite / adjacent = sin θ / cos θ
Reciprocal Functions
- Cosecant (csc θ) = 1 / sin θ = hypotenuse / opposite
- Secant (sec θ) = 1 / cos θ = hypotenuse / adjacent
- Cotangent (cot θ) = 1 / tan θ = adjacent / opposite
Special Angles
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | √3/3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
Real-World Applications
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Navigation: Calculate bearings and distances
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Physics: Analyze wave motion and oscillations
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Engineering: Design structures and calculate forces
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Astronomy: Measure celestial positions and distances
Quick Tips
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Unit
Circle
All trig functions can be visualized on the unit circle (radius = 1). -
SOH-CAH-TOA
Memory aid: Sin=Opp/Hyp, Cos=Adj/Hyp, Tan=Opp/Adj -
Radians vs Degrees
π radians = 180°. Most advanced math uses radians.
Key Identities
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = csc²θ
- sin(2θ) = 2sin(θ)cos(θ)
Trigonometry
Trigonometry is the study of relationships between angles and sides of triangles. It's essential for physics, engineering, and computer graphics.
Function Ranges
sin & cos
Range: [-1, 1]
tan & cot
Range: (-∞, ∞)
csc & sec
Range: (-∞, -1] ∪ [1, ∞)
Learn More
Did You Know?
The word "trigonometry" comes from Greek: "trigonon" (triangle) + "metron" (measure). Ancient astronomers used it to calculate distances to stars!