sen 7 30 sen cos 7 30 cos 15 2 1 15 2 1 0 9659 2 0 9914 cos 15 2 1 15 2 1 0

Sen 7 30 sen cos 7 30 cos 15 2 1 15 2 1 0 9659 2 0

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sen 7° 30 ' = sen cos 7° 30 ' = cos 15 2 1 15 2 1 0 9659 2 0 9914 ° ° = + = + = cos , , 15 2 1 15 2 1 0 9659 2 ° ° 0,1305 = = = cos , 073 tg tg tg tg 45 30 1 45 30 1 3 3 1 3 3 2 3 ° ° ° ° + = + = · 2 2 3 2 2 2 1 2 6 2 4 · · + = + 2 2 3 2 2 2 1 2 6 2 4 · · = tg tg tg tg 45 60 1 45 60 1 3 1 3 2 3 ° ° ° ° + = + = − − · 2 2 1 2 2 2 3 2 2 6 4 · · = 2 2 1 2 2 2 3 2 2 6 4 · · + = + tg tg tg tg 30 45 1 30 45 3 3 1 1 3 3 2 3 ° ° ° ° + = + = + · 3 2 2 2 1 2 2 2 6 2 4 · · = 1 2 2 2 3 2 2 2 2 6 4 · · + = + 072 Trigonometría
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137 tg 7° 30 ' = tg sen 210° = sen (2 105°) = 2 sen 105° cos 105° = cos 210° = cos (2 105°) = cos 2 105° sen 2 105° = tg 210° = tg (2 105°) = Halla las razones de 67° 30 ' , 195° y 52° 30 ' . Comprueba los resultados con la calculadora. sen (67° 30 ' ) = sen (60° + 7° 30 ' ) = sen 60° cos 7° 30 ' + cos 60° sen 7° 30 ' = cos (67° 30 ' ) = cos (60° + 7° 30 ' ) = cos 60° cos 7° 30 ' sen 60° sen 7° 30 ' = tg (67° 30 ' ) = tg (60 + 7° 30 ' ) = sen 195° = sen (210° 15°) = sen 210° cos 15° cos 210° sen 15° = = − 0,5 0,9659 ( 0,8660) 0,2588 = − 0,2588 cos 195° = cos (210° 15°) = cos 210° cos 15° + sen 210° sen 15° = = − 0,8660 0,9659 + ( 0,5) 0,2588 = − 0,9659 tg 195° = tg (210° 15°) = sen 52° 30 ' = sen cos 52° 30 ' = cos tg 52° 30 ' = tg 105 2 1 105 1 105 1 0 2588 1 0 2 ° ° ° = + = − − + − cos cos ( , ) ( , 588 1 3032 ) , = 105 2 1 105 2 1 0 2588 2 0 6088 ° ° = + = + − = cos ( , ) , 105 2 1 105 2 1 0 2588 2 0 7933 ° ° = = − − = cos ( , ) , tg tg tg tg 210 15 1 210 15 0 5773 0 2679 1 0 ° ° ° ° + = + , , , , , 5773 0 2679 0 2679 = tg tg tg tg 60 1 60 3 0 1316 1 3 0 ° 7° 30 ° 7° 30 + = + ' ' , , 1316 2 4142 = , = = 1 2 0 9914 3 2 0 1305 0 3827 , , , = + = 3 2 0 9914 1 2 0 1305 0 9239 , , , 074 2 105 1 105 2 2 3 1 2 3 3 3 2 2 · ( ) ( ) tg tg ° ° = − − = = + = − 2 6 4 2 6 4 3 2 2 2 = + = − 2 2 6 4 2 6 4 0 5 , 15 2 1 15 1 15 1 0 9659 1 0 9659 0 13 ° ° ° = + = + = cos cos , , , 16 3 SOLUCIONARIO
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138 Sabemos que sen 56° = 0,83 y cos 23° = 0,92. a) Calcula el resto de razones de esos ángulos. b) Halla las razones trigonométricas de 79°. c) Determina las razones de 33°. d) ¿Podrías hallar las razones de 28°? e) ¿Y las de 46°? a) 0,83 2 + cos 2 56° = 1 cos 56° = = 0,56 tg 56° = sen 2 23° + 0,92 2 = 1 sen 23° = = 0,39 tg 23° = = 0,42 b) sen 79° = sen (56° + 23°) = sen 56° cos 23° + cos 56° sen 23° = = 0,83 0,92 + 0,56 0,39 = 0,98 cos 79° = cos (56° + 23°) = cos 56° cos 23° sen 56° sen 23° = = 0,56 0,92 0,83 · 0,39 = 0,19 tg 79° = tg (56° + 23°) = c) sen 33° = sen (56° 23°) = sen 56° cos 23° cos 56° sen 23° = = 0,83 0,92 0,56 0,39 = 0,55 cos 33° = cos (56° 23°) = cos 56° cos 23° + sen 56° sen 23° = = 0,56 · 0,92 + 0,83 0,39 = 0,84 tg 33° = tg (56° 23°) = d) sen 28° = sen cos 28° = cos tg 28° = tg e) sen 46° = sen (2 23°) = 2 sen 23° cos 23° = 2 0,39 0,92 = 0,72 cos 46° = cos (2 23°) = cos 2 23° sen 2 23° = 0,92 2 0,39 2 = 0,69 tg 46° = tg (2 23°) = Obtén una fórmula simplificada de: a) sen (30° + $ A ) c) tg (45° $ C ) b) cos ( $ B 60°) d) cos ( $ D + 30°) 076 2 23 1 23 2 0 42 1 0 42 1 02 2 2 · · , , , tg tg ° ° = = 56 2 1 56 1 56 1 0 56 1 0 56 0 53 ° ° ° = + = + = cos cos , , , 56 2 1 56 2 1 0 56 2 0 88 ° ° = + = + = cos , , 56 2 1 56 2 1 0 56 2 0 47 ° ° = = = cos , , tg tg tg tg 56 23 1 56 23 1 48 0 42 1 1 48 0 ° ° ° ° + = + , , , , 42 0 65 = , tg tg tg tg 56 23 1 56 23 1 48 0 42 1 1 48 0 ° ° ° ° + = + , , , , 42 5 02 = , 0 39 0 92 , , 1 0 92 2 , 0 83 0 56 , , = 1,48 1 0 83 2 , 075 Trigonometría
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139 a) sen (30° + $ A ) = sen 30° cos $ A + cos 30° sen $ A = cos $ A +
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