Bevis: - synd (7 theta) + synd (5 theta) / synd (7 theta) -sin (5 theta) =?
(sin7x + sin5x) / (sin7x-sin5x) = tan6x * cotx rarr (sin7x + sin5x) / (sin7x-sin5x) = (2sin ((7x + 5x) / 2) * cos ((7x-5x) / 2) ) / (2sin ((7x-5x) / 2) * cos ((7x + 5x) / 2) = (sin6x * cosx) / (sinx * cos6x) = (tan6x) / tanx = tan6x * cottx
Hvad er ligningen af tangentlinjen af r = tan ^ 2 (theta) - sin (theta-pi) ved theta = pi / 4?
R = (2 + sqrt2) / 2r = tan ^ 2-thetan (theta-pi) ved pi / 4r = tan ^ 2 (pi / 4) - sin (pi / 4 -pi) r = 1 ^ 2 - synd ((- 3pi) / 4) r = 1-sin ((5pi) / 4) r = 1 - (- sqrt2 / 2) r = 1 + sqrt2 / 2 r = (2 + sqrt2) / 2
Hvordan udtrykker du f (theta) = sin ^ 2 (theta) + 3cot ^ 2 (theta) -3csc ^ 2theta i form af ikke-eksponentielle trigonometriske funktioner?
Se nedenfor f (theta) = 3sin ^ 2teta + 3cot ^ 2teta-3csc ^ 2theta = 3sin ^ 2ta + 3cot ^ 2ta-3csc ^ 2theta = 3sin ^ 2ta + 3 (csc ^ 2theta-1) -3csc ^ 2theta = 3sin ^ 2theta + annullere (3csc ^ 2theta) -cancel3csc ^ 2theta-3 = 3sin ^ 2theta-3 = -3 (1-sin ^ 2theta) = -3cos ^ 2theta