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Instituto de Ciencias - UNGS I NTRODUCCIÓN A LA M ATEMÁTICA Guía de TP No 6


Práctica 6 - Funciones Trigonométricas.
1. Completar la siguiente tabla, convirtiendo a radianes o a grados según corresponda:

Grados 30◦ 180◦ 10◦ 1◦
2 π
Radianes π 3π 4 1

2. Dados los siguientes arcos medidos en radianes y los siguientes ángulos medidos en grados sexage-
simales:

t1 = π α = 30◦ t4 = −π β = 50◦ γ = 90◦ t9 = −1
t2 = 5π t3 = 52 π t5 = π
3 t6 = − π2 t8 = 1 t10 = 1
2

a) Indicar cuál es el punto que determina en la circunferencia trigonométrica.
b) ¿Cuáles son las coordenadas (x, y) del punto de la circunferencia trigonométrica que determina
el arco t1 ? Responder la misma pregunta para el ángulo γ y para el arco t6 .
c) Calcular el seno y el coseno de t1 , t4 y t6 .

3. En el siguiente gráfico se puede observar: una circunferencia de radio uno, el arco de circunferencia
(con origen en el (1, 0)) de longitud T y las coordenadas del punto que determina P = (a, b).




a) A partir de este gráfico expresar las cantidades siguientes utilizando a y b:

(i) sen(T ) (v) sen(T + 2π)
(ii) cos(T ) (vi) cos(T + π)
(iii) sen(−T ) (vii) sen(π − T )
(iv) cos(−T ) (viii) cos(π − T )

b) Hallar todas las longitudes de arco x en el intervalo [0, 2π] que cumplen la igualdad sen(x) = b.
c) Hallar todas las longitudes x en el intervalo [0, 2π] que cumplen la igualdad cos(x) = a.





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