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Clase 69

Clase 69. sen x. cos x. tan x =. cot x =. cos x. sen x. Fórmulas de adición. sen(x + y) = ?. sen 2 x + cos 2 x = 1. cos(x + y) = ?. cos(x – y) = ?. sen(x – y) = ?. √ 3. 12. +. =. 2. sen(x + y) = sen x + sen y. F a l s o. Sean x = 30 0 y y = 60 0. = sen 90 0.

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Clase 69

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  1. Clase 69 sen x cos x tan x = cot x = cos x sen x Fórmulas de adición sen(x + y) = ? sen2x + cos2x = 1 cos(x + y) = ? cos(x – y) = ? sen(x – y) = ?

  2. √3 12 + = 2 sen(x + y) = sen x + sen y F a l s o Sean x = 300 y y = 600 = sen 900 sen(300 +600) = 1 sen 300 + sen 600  0,5 + 0,866  1,366

  3. CS  OB SN  OA sen(x+y) = CM cos(x+y) = OM NS = MR y C x B R S x + y y x A 0 N x M

  4. y C sen(x+y) = CM B x R S y x x A M N MR = sen x  cos y OS = cos y CS = sen y MR= NS CR = cos x  sen y CM = MR + CR CR = CS  cos x = OS sen x CM = sen x  cos y + cos x  sen y sen(x+y) = sen x cos y + cos x sen y pero luego, O pero luego, 

  5. y C B x R cos(x+y) = OM S y x O x A M N OS = cos y CS = sen y ON = cos x cos y MN = RS OM = ON – MN MN = sen x sen y = CS  sen x ON = OS cos x OM = cos x cos y – sen x sen y cos(x+y) = cos x cos y – sen x  sen y pero, luego, pero, luego, 

  6. sen(x+y) = sen x cos y + cos x sen y cos(x+y) = cos x cos y – sen x  sen y sen(x–y)=senxcos(–y)+cosxsen (–y) pero, cos(–y) = cos y sen(–y) =– sen y sen(x – y)= sen x cos y – cos x sen y cos(x–y)=cosxcos(–y)–senxsen (–y) cos(x – y)= cos x cos y + sen x sen y

  7. tan x + tan y tan(x + y) = 1 – tan x tan y tan x – tan y tan(x – y) = 1 + tan x tan y

  8. Ejercicio Sabiendo que: sen 500 = 0,7660; cos 500 = 0,6428; Calcula: a) sen(–200) b) cos 820 sen 700 = 0,9397; cos 700 = 0,4320; sen 120 = 0,2079; cos 120 = 0,9781.

  9. = sen (500 – 700) a) sen(–200) = sen500cos700 – cos500 sen700 –( 0,6428) (0,9397) (0,342) = (0,766) = 0,26197 – 0,60403 = – 0,34206  – 0,3421 – 0,342

  10. = sen (700 + 120) b) cos(820) = cos700cos120 – sen700 sen120 =(0,342) (0,9781) –( 0,9397) (0,2079) = 0,33451 – 0,19536 = 0,13915  – 0,1392 – 0,139

  11. Para el estudio individual Utilizando las fórmulas de adición y los valores notables de las razones trigonométricas de los ángulos notables. Calcula las razones trigonométricas de los ángulos 150, 750y 1050. Verifica tus resultados con las tablas.

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