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Sagot :
Answer:
sen α = - 4/5
cos α = - 3/5
Step-by-step explanation:
tang α = 4/3
De la relación fundamental de la trigonometría sabemos:
sen² α + cos²α = 1
Dividiendo la ecuación anterior por cos² α
sen²α/cos²α + cos²α / cos²α = 1 / cos² α
tang²α + 1 = 1/ cos² α
(4/3)² + 1 = 1/ cos² α ⇒ 16/9 + 1 = 1/ cos² α
1/ cos² α = ( 16 + 9 ) / 9
1/ cos² α = 25/9
cos² α = 9/25
cos α = 3/5
y para calcular el sen α
sen² α = 1 - cos²α
sen² α = 1 - 9/25
sen² α = ( 25 - 9 )/ 25
sen² α = 16/25
sen α = 4 / 5
Ahora bien el angulo α está en el tercer cuadrante, en ese cuadrante tanto el seno como el coseno son negativos.
Respuesta:
sen α = - 4/5
cos α = - 3/5
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