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sin(θ)
0.707
cos(θ)
0.707
tan(θ)
1
csc(θ)
1.414
sec(θ)
1.414
cot(θ)
1
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View detailed breakdowns and explanations below.
📘 What is Trigonometry?
Trigonometry is the study of relationships between angles and sides of triangles. The word comes from Greek: "trigonon" (triangle) + "metron" (measure).
🎓 The Six Trig Functions
- Sine (sin): opposite / hypotenuse
- Cosine (cos): adjacent / hypotenuse
- Tangent (tan): opposite / adjacent
- Cosecant (csc): 1 / sin
- Secant (sec): 1 / cos
- Cotangent (cot): 1 / tan
💡 Key Identities
sin²(θ) + cos²(θ) = 1
tan(θ) = sin(θ) / cos(θ)
sin(2θ) = 2sin(θ)cos(θ)
cos(2θ) = cos²(θ) - sin²(θ)
🚀 Applications
- Navigation: GPS, surveying, and astronomy
- Physics: Wave motion, oscillations, and mechanics
- Engineering: Structural analysis and signal processing
- Computer Graphics: 3D rotations and transformations
- Music: Sound wave analysis and synthesis
⚡ Quick Reference
Special angles to memorize:
- sin(30°) = 1/2, cos(30°) = √3/2
- sin(45°) = cos(45°) = √2/2
- sin(60°) = √3/2, cos(60°) = 1/2
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