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Obdobje greha 6t ->
Obdobje cos 39t ->
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Obdobje f (t) ->
Pogostost f (t) ->
Dokazilo: - sin (7 theta) + sin (5 theta) / sin (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
Kakšen je naklon polarne krivulje f (theta) = theta - sec ^ 3 theta + thetasin ^ 3theta pri theta = (5pi) / 8?
Dy / dx = -0,54 Za polarno funkcijo f (theta), dy / dx = (f '(theta) sintheta + f (theta) costheta) / (f' (theta) costheta-f (theta) sintheta) f ( theta) = theta-sec ^ 3theta + thetasin ^ 3theta f '(theta) = 1-3 (sec ^ 2theta) (d / dx [secteta]) - sin ^ 3 theta + 3thetasin ^ 2theta (d / dx [sintheta]) f '(theta) = 1-3sec ^ 3tetatantheta-sin ^ 3theta + 3thetasin ^ 2thetacostheta f' ((5pi) / 3) = 1-3sec ^ 3 ((5pi) / 3) tan ((5pi) / 3) - sin ^ 3 ((5pi) / 3) +3 ((5pi) / 3) sin ^ 2 ((5pi) / 3) cos ((5pi) / 3) ~~ -9.98 f ((5pi) / 3) = ((5pi) / 3) -sec ^ 3 ((5pi) / 3) + ((5pi) / 3) sin ^ 3 ((5pi) / 3) ~~ -6.16
Kako dokazujete 1 / (1 + sin (theta)) + 1 / (1-sin (theta)) = 2sec ^ 2 (theta)?
Glej spodaj LHS = leva stran, RHS = desna stran LHS = 1 / (1 + sin theta) + 1 / (1-sin theta) = (1-sin theta + 1 + sin theta) / ((1 + sin) theta) (1-sin theta)) -> skupni imenovalec = (1-ponižujoči se theta + 1 + kaneli v theta) / ((1 + sin theta) (1-sin theta)) = 2 / (1-sin ^ 2x) = 2 / cos ^ 2x = 2 * 1 / cos ^ 2x = 2sec ^ 2x = RHS