d Sin determinar el ángulo x decide razonadamente en qué cuadrante están los

D sin determinar el ángulo x decide razonadamente en

This preview shows page 141 - 144 out of 640 pages.

d) Sin determinar el ángulo x , decide razonadamente en qué cuadrante están los ángulos. a) cos x = sen 2 x + 0,8 2 = 1 sen x = = − 0,6 b) sen cos tg sen cos tg c) d) Como el seno del ángulo x es positivo, el ángulo está en el 2. o cuadrante. Y como la tangente del ángulo x + es positiva, el ángulo está en el 3. er cuadrante. Sabiendo que las razones de 32° son: sen 32° = 0,53 cos 32° = 0,848 a) Calcula las razones trigonométricas de 62°. b) Halla las razones de 31°. c) ¿Puedes medir cualquier ángulo cuya medida en grados no tenga minutos ni segundos? c) Sí podemos calcular las razones de cualquier ángulo, ya que a partir de las medidas de 32° y de 31° hallamos las medidas de 1°, y a partir de ellas, las demás. b) 31° 62° 2 ° 2 0,46 2 sen sen cos cos = = = = 1 62 1 0 52 3 , 1 62 2 1 62 1 0 85 31 ° ° ° 2 0,46 2 ° 0,5 = = + = + = = cos cos tg , 2 0,85 0,61 = a) 62° 32° 30° 32° 30° 32° sen sen sen cos cos = + = + ( ) sen cos cos 30° 0,53 3 0,848 0,88 62° 32 = = + = = 2 1 2 ( ° 30° 32° 30° 32° 30° + = = = ) , cos cos sen sen 0 848 3 2 0 53 1 2 0 46 = = = , , tg 62° 0,88 0,46 1,91 081 π 6 π 4 tg x tg x tg tg x tg + = + = + π π π 6 6 1 6 3 4 3 3 1 · = + 3 4 3 3 48 25 3 39 · cos cos cos x x sen x sen = + = − π π π 4 4 4 0 , , , 8 2 2 0 6 2 2 0 7 2 = − π 4 1 = π 4 2 2 = π 4 2 2 = π 6 3 3 = π 6 3 2 = π 6 1 2 = 1 0 8 2 , 1 1 0 75 0 8 2 + = − , , x + π 6 x π 4 tg x + π 6 cos x π 4 3 SOLUCIONARIO
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142 Expresa en función de la razón de un solo ángulo. 1 + cos + cos α = sen 2 + cos 2 + cos + cos 2 sen 2 = = 2 cos 2 + cos Demuestra que se verifican estas igualdades. a) 1 + sen 2 α= 2 sen ( α+ 45°) cos ( α− 45°) b) cos 2 α= 2 sen ( α+ 45°) cos ( α+ 45°) a) 2 sen ( α + 45°) cos ( α − 45°) = = 2 ( sen α ⋅ cos 45° + cos α ⋅ sen 45°)( cos α ⋅ cos 45° + sen α ⋅ sen 45°) = = cos 2 α + sen 2 α + 2 sen α ⋅ cos α = 1 + sen 2 α b) 2 sen ( α + 45°) cos ( α + 45°) = = 2 ( sen α ⋅ cos 45° + cos α ⋅ sen 45°)( cos α ⋅ cos 45° sen α ⋅ sen 45°) = = cos 2 α − sen 2 α = cos 2 α Comprueba la siguiente relación entre las razones trigonométricas de un ángulo. Demuestra que es cierta la igualdad. sen sen cos sen cos cos tg cos 2 2 2 2 1 2 2 α α α α α α α α = = = = + 2 1 2 tg tg α α sen tg tg 2 2 α α α = + 1 2 085 1 2 2 2 2 2 2 = = = cos x sen x sen x sen x cos x sen x cos x tg x 1 2 2 = cos x sen x tg x 2 084 = 2 2 4 2 4 2 2 cos sen α α = + 2 2 2 2 2 2 2 2 sen cos cos sen α α α α 2 = = + + 2 2 4 4 4 2 4 2 2 cos sen cos sen α α α α = = + + 2 2 2 2 2 2 2 2 sen cos cos sen α α α α 2 = 083 α 2 α 2 α 2 α 2 α 2 α 2 α 2 α 2 1 2 + + cos cos α α 082 Trigonometría
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