Solve the following equations in the interval 0 2 pi tan x

Solve the following equations in the interval [0, 2 pi) tan x - Squareroot 3 = 0 2Cos(x) + 1 = 0 Divide 6 x^3 - 19 x^2 + 16 x - 4 by x - 2 and determine the zeros of a polynomial f(x) = 6x^3 - 19x^2 + 16x - 4 Simplify: (2 + 7 i) + (Squareroot 2 - i)

Solution

a) tanx - sqrt3 =0

tanx = sqrt3

x = tan^-1(sqrt3) = pi/3 , pi+pi/3

Interval [0, 2pi ) x = pi/3 , 4pi/3

b) 2cosx +1 =0

cosx = -1/2

x = cos^-1(-1/2) = pi - pi/3 , pi +pi/3

x = 2pi/3 , 4pi/3