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Primary Functions
sin(θ):0.707
cos(θ):0.707
tan(θ):1
Reciprocal Functions
csc(θ):1.414
sec(θ):1.414
cot(θ):1
Common Angles
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View detailed breakdowns and explanations below.
📘 The Six Trigonometric Functions
For any angle θ in a right triangle:
- sin(θ): opposite / hypotenuse
- cos(θ): adjacent / hypotenuse
- tan(θ): opposite / adjacent
- csc(θ): hypotenuse / opposite = 1/sin(θ)
- sec(θ): hypotenuse / adjacent = 1/cos(θ)
- cot(θ): adjacent / opposite = 1/tan(θ)
🎓 Unit Circle Definition
On the unit circle, for a point at angle θ:
- sin(θ): y-coordinate
- cos(θ): x-coordinate
- tan(θ): slope of the radius (y/x)
💡 Relationships
tan(θ) = sin(θ) / cos(θ)
cot(θ) = cos(θ) / sin(θ)
sin²(θ) + cos²(θ) = 1
🚀 Applications
- Geometry: Solving triangles and finding angles
- Physics: Wave motion, oscillations, and circular motion
- Engineering: Signal processing and structural analysis
- Navigation: GPS, surveying, and astronomy
- Computer Graphics: Rotations and transformations
⚡ Memory Aid: SOH-CAH-TOA
- SOH: Sine = Opposite / Hypotenuse
- CAH: Cosine = Adjacent / Hypotenuse
- TOA: Tangent = Opposite / Adjacent
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