Find the general solution, in radians, of the equation cos5x=sinx?

Answer 1

cos5x = sinx
cos5x = cos(pi/2 - x)
5x = 2npi +- (pi/2 - x)
6x = (4n + 1)pi/2 , 4x= (4n-1)pi/2
x= (4n+1)pi/12 , x = (4n-1)pi/8

Answer 2

?3/(?(9+y^2 ))dy=?4xdx ----- (a million) combine the left side permit y = 3 sinh(t) dy=3 cosh(t) dt 9+y^2=9+9 sinh^2(t) = 9(a million+sinh^2 (t)) = 9 cosh^2(t) sqrt(9+y^2)=sqrt(cosh^2(t)) = 3 cosh(t) ?3/(?(9+y^2 ))dy = ? 3 [3 cosh(t) dt] / 3cosh(t) = 3 ? dt = 3 t+C = 3 sinh^-a million(y/3) ?4xdx = 2x^2 (a million) will become: 3 sinh^-a million(y/3) = 2x^2 + C sinh^-a million(y/3) = (a million/3) {2x^2+C] y/3 = sinh[ (a million/3) (2x^2 + C)] y = 3 sinh[ (a million/3) (2x^2 + C)] it is the final answer