Oh, dude, we're getting all mathy up in here! So, to solve this bad boy, you can divide both sides by sin(x) to get tan(x) = 7/3. Then, you can take the arctan of both sides to find x. Just make sure you're in the right quadrant, like, don't go wandering off into negative angles, man.
+3 and -3
8
With respect to x, this integral is (-15/2) cos2x + C.
y=-3x*sinx-1.5x2+5x, when x=πy'=d/dx(-3x*sinx)-d/dx(1.5x2)+d/dx(5x)y'=(-3x*d/dx(sinx)+sinx*d/dx(-3x))-d/dx(1.5x2)+d/dx(5x)y'=(-3x*cosx+sinx(-3))-d/dx(1.5x2)+d/dx(5x)y'=(-3x*cosx-3sinx)-3x+5y'=-3x*cosx-3sinx-3x+5 is the derivative at any point of that equation, now you only have to plug in π for xy'(π)=-3π*cosπ-3sinπ-3π+5y'(π)=-3π*(-1)-3(0)-3π+5y'(π)=3π-3π+5y'(π)=5
If y = 3sin(x)3, and x has no limit, then y has a range of -3 to 3.
d(cos−13 + 5cosx5 + 3cosx)/dx = −1/2(1−32) − 25x4sinx5 − 3sinx
The sine function (sin x) can only have values in the range between 1 and -1. Perhaps you can work it out from there.
The only variable on the right hand side is sin(x). The maximum value of sin(x) is 1. So, the max value of 3sin(x) is 3*1 = 3 and so, the max value of 3sin(x) + 2 is 3+2 = 5.
looks like the exponents did not show up, in the first it should be 4 cosine cubed x - 3cosx and the sin 3x should be 3sinx - 4sine cubed x
2sinx - sin3x = 0 2sinx - 3sinx + 4sin3x = 0 4sin3x - sinx = 0 sinx(4sin2x - 1) = 0 sinx*(2sinx - 1)(2sinx + 1) = 0 so sinx = 0 or sinx = -1/2 or sinx = 1/2 It is not possible to go any further since the domain for x is not defined.
sinx = sin0 = 0 tanx = tan0 = 0 you have 0/0 by you limit conditions
According to de Moivre's formula, cos3x + isin3x = (cosx + isinx)3 = cos3x + 3cos2x*isinx + 3cosx*i2sin2x + i3sin3x Comparing the imaginary parts, isin3x = 3cos2x*isinx + i3sin3x so that sin3x = 3cos2x*sinx - sin3x = 3*(1-sin2x)sinx - sin3x = 3sinx - 4sin3x