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Sumario Resumen sobre coseno de alfa
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Coseno (cos): DefiniciónEl coseno es una función trigonométrica que relaciona el ángulo de un triángulo
rectángulo con la longitud de sus lados. En un triángulo rectángulo, el coseno de un
ángulo agudo (α) se define como el cociente entre el cateto adyacente al ángulo y la
hipotenusa.
La notación para el coseno de un ángulo α es cos(α).
Fórmula del Coseno:
En un triángulo rectángulo con un ángulo agudo α, la fórmula del coseno se expresa
𝐶𝑎𝑡𝑒𝑡𝑜 𝐴𝑑𝑦𝑎𝑐𝑒𝑛𝑡𝑒
como: cos(α)= 𝐻𝑖𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑎
Propiedades Importantes del Coseno:
El coseno de un ángulo agudo siempre está en el rango[−1,1].
1. −1≤cos(α)≤1
2. El coseno de 0 grados es 1:cos(0)=1.
3. El coseno de 90 grados es 0: cos(90∘)=0.
Identidades Trigonométricas:
- Identidad Fundamental:
cos2(α)+sin2(α)=1
- Relación Recíproca:
cos(α)=1sec(α)
- Identidad Par:
cos(−α)=cos(α)
- Identidad Impar:
π
cos( 2 - α)=sin(α)
Estos son algunos conceptos básicos sobre el coseno y sus propiedades. Recuerda
que el coseno es una función fundamental en la trigonometría y tiene aplicaciones
en diversos campos como la física, la ingeniería y la informática.
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