Help with math trig

[KarimA]

Hello everyone, I don't know how to solve the following: (i edited cuz i didnt know how to put the pi expression)

 

1)                  Find the values of x if x between [0 and 2pi] in the following expression

 

                        i)             2cos2x - 7cosx=0                       ii) -1 + sin2x + 2cosx - sinx=0

 

 and Rad(2)sinxtanx - rad(6)sinx -tanx + rad(3)=0

[SYL]

i) Since cos2x = 2cos^2x -1, expand it out to obtain the quadratic 4cos^2x -7cosx -2 = 0 then solve.

 for ii), you also have to find a way to factorise.
ie. -1 + 2sinxcosx + 2cosx - sinx = 0
                     2cosx(sinx +1) -(sinx+1) = 0    (sinx+1) is a common factor so

                  (sinx +1) ( 2cosx -1) = 0
               then solve for x, noting that is is between 0 and 2pi.

 

for the last one it is the same as ii), Find a common factor and factorise further by finding another common factor

   the first step is: √2sinx ( tanx -√3) -(tanx -√3) = 0

Edited April 9, 2015 by SYL