Unidad 2 pensamiento variaciones y trigonométrico:ley del seno
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This document defines trigonometric functions using right triangles and explains the Law of Sines. It gives definitions for sine, cosine, tangent, cosecant, and secant in terms of the sides of a right triangle and associated angles. It then presents an example problem using the Law of Sines to solve for the measures of an unknown side and angle of a triangle given the measures of two sides and one angle. The example finds the missing side to be 11.54 meters.
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- 1. Unidad 2 pensamiento variaciones y trigonométrico: ley del seno Paola Andrea Sánchez Patiño algebra trigonometría y geometría 551108A_954 GRUPO55 1108_20 TUTOR HENRY ALBEIROSÁENZ
- 3. Funciones trigonometrías: se definen comúnmente como el cociente entre dos lados de un triangulo rectangulo,asociado a sus ángulos para una mejor interpretación de esta definición podemos representar la noción trigonométrica de seno, coseno y tangente de un Angulo asi: B A C b a c
- 4. Funciones trigonométricas entonces; las funciones trigonométricas quedan definidas de la siguiente manera: senA= a = cateto opuesto cotgA= b = cateto adyacente c hipotenusa a cateto opuesto cosA= b cateto adyacente secA= c = hipotenusa c hipotenusa b cateto adyacente tgA= a = cateto opuesto cosecA = hipotenusa b cateto adyacente cateto opuesto
- 5. LEYES DE LAS FUNIONES TRIGONOMETRIAS Ley del seno: a = b = C senA senB senC Ley de los cosenos :𝑐2 = 𝑎2 + 𝑏2 -2abcosC ley de las tangentes: a+b =tg 1/2 (A+B) a-b tg 1/2 ( A-B)
- 6. LEY DEL SENO: a b c senA senB senC ejercicio desarrollar el siguiente ejercicio aplicando la ley del seno a=10m b = 6m =120° este teorema relaciona los lados de un triangulo con sus ángulos respectivos a = b = c senA senB senC ANGULO LADO A=120 A=10m B=? B=6m C=? C=?
- 7. Ejercicio: a b c senA senB senC reemplazamos: 10m = 6 sen120 ° Sen B Sen B = Sen 120°.6m 10m *SenB = 6m *Sen B 10 m Sen 120° = Sen B Sen B = 3 2 . 6 m 10m 10 m Sen 120° * SenB = 6m Sen B = 3 3 10 𝑚 10m 6m Sen 120° * Sen B = 1 Sen B = 0,519 10m 10m Sen −1 0,519 = B Sen 120° 120° Sen B = 6m 1 B = 31.30° 10 Sen 120°
- 8. La suma de los ángulos internos de un Angulo es 180°,dado que concomeos los valores de A y B: podemos hallar el valor de C dado que A+B+C =180° 120° + 31,30° + C = 180° 151,30° + C = 180° 151,30° - 151,30° + C = 180° - 151,30° C = 28,7°
- 9. Finalmente podemos usar nuevamente el teorema del seno para hallar el valor del lado faltante C. 10 m = c Sen 120° Sen 28,7° 10m c Sen 120° * Sen 28.7° = Sen 28,7° * Sen 28,7° ° 10m Sen 120° * Sen 28.7°=C 10m 3 2 * 0,48 = C 20 3 * 0,48 = C 11,54 * 0.48 = C
- 11. Mil gracias tutor y compañeras