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TRIGONOMETRÍA<br />
Sen<br />
⎛ π ⎞ 2<br />
⎜ x − ⎟ =<br />
⎝ 3 ⎠ 2<br />
<br />
θG<br />
π<br />
θp=<br />
4<br />
x - 3<br />
π = nπ + (-1)<br />
n<br />
π<br />
4<br />
π π<br />
x = nπ + (-1) n +<br />
4 3<br />
i) n = 2k<br />
x = 2kπ +<br />
π<br />
+<br />
π →<br />
4 3<br />
7π<br />
x = 2kπ + 12<br />
ii) n = 2k + 1<br />
π<br />
x = (2k + 1) π - +<br />
π<br />
13π<br />
→ x = 2kπ +<br />
4 3<br />
12<br />
4. 2Cos 2x – Sen3x = 2<br />
RESOLUCIÓN<br />
2(1-2Sen²x) – (3Senx – 4Sen3x) = 2<br />
4Sen²x – 4Sen²x – 3 Senx = 0<br />
Sen x (4Sen² x – 4 Senx - 3) = 0<br />
Senx (2Sen x - 3) (2Senx + 1) = 0<br />
i) Sen x = 0<br />
x = nπ<br />
ii) Senx = - 2<br />
1<br />
π<br />
x = nπ - (-1) n 6<br />
iii) Sen x = 2<br />
3 → ABSURDO<br />
5. Senx + Sen2x + Sen3x = Cosx + Cos2x + Cos3x<br />
RESOLUCIÓN<br />
2Sen2x . Cosx + Sen2x = 2 Cos2x . Cosx + Cos2x<br />
Sen2x (2Cosx + 1) = Cos2x (2Cosx + 1)<br />
Queda:<br />
Sen2x = Cos 2x<br />
Tg 2x = 1<br />
π<br />
θ p = 4<br />
θ G<br />
2x = nπ+ 4<br />
π<br />
Pero → 2Cosx + 1 = 0<br />
Cosx = - ½<br />
→ x =<br />
nπ<br />
π<br />
+<br />
2 8<br />
CUESTIONARIO DESARROLLADO
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