sen x cos x 1 1 x k x k 1 2 x k x k x k 1 2 3 90 360 270 360 210 360

Sen x cos x 1 1 x k x k 1 2 x k x k x k 1 2 3 90 360

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° ° ° ° · · sen x cos x 1 1 0 + = x k x k 1 2 0 180 90 180 = + = + ° ° ° ° · · x k x k x k 1 2 3 90 360 270 360 210 = + = + = + ° ° ° ° ° = + 360 330 360 4 ° ° ° x k x k x k 1 2 22 5 180 112 5 180 = + = + , · , · ° ° ° ° x k x k 1 2 45 360 225 360 = + = + ° ° ° ° · · x k x k 1 2 0 360 180 360 = + = + ° ° ° ° · · x k x k 1 2 30 360 150 360 = + = + ° ° ° ° · · 1 2 1 2 tg x tg x π 4 1 0 + = sen x cos x ( ° 60 1 = ) cos x tg x = 1 2 091 Trigonometría
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145 i) tg + tg x 1 = 0 + tg x 1 = 0 tg 2 x tg x = 0 tg x ( tg x 1) = 0 tg x = 0 tg x 1 = 0 tg x = 1 j) sen ( x + 30°) + cos ( x + 60°) = 1 + cos 2 x = cos 2 x + sen 2 x + cos 2 x sen 2 x cos x = 2 cos 2 x cos x (2 cos x 1) = 0 cos x = 0 2 cos x 1 = 0 cos x = Resuelve estos sistemas de ecuaciones trigonométricas. cos 2 y = sen 2 30° cos y = y = 60° + 180° k cos 2 y + sen y cos y = 1 + sen y cos y sen 2 y cos 2 y sen 2 y = 1 cos 2 y = − 1 y = 90° + 180° k x = 120° y = 120° 90° 180° k = 30° 180° k 3 3 b) x y cos x cos y sen x tg y + = = + 120 1 2 ⎯⎯⎯ ⎯→ x y cos y cos y sen y t = = = + 120 120 1 2 120 ° ° ° ( ) ( ) g y 1 4 a) sen x sen y cos x cos y se 2 2 2 2 1 1 2 + = = n x sen y cos y cos x sen x 2 2 2 2 2 1 1 2 = = = cos x x k 2 1 2 30 180 = = + ° ° · b) 2 x y cos x cos y sen x tg y + = = + 120 1 a) sen x sen y cos x cos y 2 2 2 2 1 1 2 + = = 092 x k x k 1 2 60 360 300 360 = + = + ° ° ° ° · · 1 2 x k x k 1 2 90 360 270 360 = + = + ° ° ° ° · · 3 2 2 2 3 2 sen x cos x cos x sen x + + = x k x k 1 2 45 360 225 360 = + = + ° ° ° ° · · x k x k 1 2 0 360 180 360 = + = + ° ° ° ° · · 1 1 + tg x tg x π 4 x 3 SOLUCIONARIO
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146 Resuelve las ecuaciones trigonométricas. a) 4 sen x sec x = 0 b) c) d) sen x ( sen x 1) = 5 cos 2 x 4 e) 2 cos x 1 = sec x f ) 2 cos x + sen x = 1 g) sen x + cos x = 0 a) 4 sen x sec x = 0 4 sen x cos x 1 = 0 2 sen 2 x = 1 sen 2 x = b) = sen x cos 2 x = 2 cos x sen x + sen 2 x cos 2 x = sen 2 x c) + 2 sen x = 2 cos x = 1 = 1 tg x = 1 d) sen x ( sen x 1) = 5 cos 2 x 4 sen 2 x sen x = 5(1 sen 2 x ) 4 6 sen 2 x sen x 1 = 0 sen x = sen x = e) 2 cos x 1 = sec x 2 cos 2 x cos x 1 = 0 cos x = 1 cos x = f) 2 cos x + sen x = 1 = 1 2 cos x 5 cos 2 x 4 cos x = 0 cos x (5 cos x 4) = 0 cos x = g) sen x + cos x = 0 sen x = − cos x x k x k 1 2 135 360 315 360 = + = + ° ° ° ° · · 4 5 36 52 11 6 360 323 7 48 4 360 1 2 x k x = + = + ° ° ° ° ' " ' " , · , · k
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