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Trigonometric functions (sin, cos, tan, csc, sec, cot) relate the angles and sides of triangles. They extend to the unit circle for all angles and are fundamental in physics, engineering, navigation, signal processing, and wave analysis.
Guia passo a passo
- 1In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
- 2Mnemonic: SOH-CAH-TOA
- 3Unit circle definition: sin θ = y-coordinate, cos θ = x-coordinate, at angle θ from positive x-axis
- 4Reciprocals: csc = 1/sin, sec = 1/cos, cot = 1/tan
Exemplos resolvidos
Entrada
sin 30°
Resultado
0.5
sin(π/6) = 1/2
Entrada
cos 60°
Resultado
0.5
cos(π/3) = 1/2
Entrada
tan 45°
Resultado
1
tan(π/4) = sin/cos = 1
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