Tarea

1. Ejercicios
Trigonometría
1. A guy wire of length 108 meters runs from the top of an antenna to the ground. If the angle of elevation of the
top of the antenna, sighting along the guy wire, is 42.3°, then what is the height of the antenna?
2. The angle of elevation of the top of a water tower from point A on the ground is 19.9°. From point B, 50.0
feet closer to the tower, the angle of elevation is 21.8°. What is the height of the tower?
3. From point A the angle of elevation to the top of the building is 30°, as shown in the accompanying figure.
From point B, 20 meters closer to the building, the angle of elevation is 45°. Find the angle of elevation of the
building from point C, which is another 20 meters closer to the building.

2. 4. Desde la punta B de una torre, el ángulo de depresión de la punta D de la otra torre, que dista 30 m de la
primera, es de 28°. Si la torre más alta mide 62 m ¿cuál es la altura de la torre menor?
5. For the triangle in the figure 𝐶 = 102° 𝐵 = 29° 𝑎𝑛𝑑 𝑏 = 28 𝑓𝑒𝑒𝑡. Find the remaining angle and sides.
6. For the triangle in the figure , 𝑎 = 22 𝑖𝑛𝑐ℎ𝑒𝑠, 𝑏 = 12 𝑖𝑛𝑐ℎ𝑒𝑠, and 𝐴 = 42° Find the remaining side and angles.

3. 7. Un satélite meteorológico que orbita el ecuador a una altura de 𝐻 = 40 000 𝑘𝑚, detecta una tormenta eléctrica al norte, en P, a un
ángulo de 𝜃 = 6.3° de su vertical. Dado que el radio de la Tierra es aproximadamente 𝑅 = 6370 𝑘𝑚, encuentre el ángulo de latitud 𝜑
de la tormenta eléctrica.
8. The course for a boat race starts at point A and proceeds in the direction S 52° W to point B, then in the direction S 40° E to point
C, and finally back to A. Point C lies 8 kilometers directly south of point A. Approximate the total distance of the race course.
Verificar las siguientes identidades:
9) tan 𝜃 cot𝜃 − 𝑠𝑒𝑛2 𝜃 = 𝑐𝑜𝑠2 𝜃 10) 𝑠𝑒𝑛 𝜃 csc 𝜃 − 𝑠𝑒𝑛2 𝜃 = 𝑐𝑜𝑠2 𝜃
Resuelva las siguientes ecuaciones trigonométricas en el intervalo [0°,360°]
11) 2 𝑠𝑒𝑛 𝜃 + 1 = 0 12) 𝑠𝑒𝑛𝜃tan 𝜃 = 𝑠𝑒𝑛 𝜃 13) 𝑡𝑎𝑛2 𝜃 + 𝑡𝑎𝑛𝜃 − 2 = 0

4. Determine las demás funciones trigonométricas a partir de:
14) 𝑠𝑒𝑛 𝛼 =
1
2
15)tan 𝛽 =
4
3
16 )cos 𝜃 =
√3
2