Solve 7 cos(2x)=7sin^2

Question

Solve  for all solutions 

 =  

 Give your answers accurate to at least 2 decimal places, as a list separated by commas

Answer 1

7cos2x =7(cos^2x - sin^2x) = 7(1 - sin^2x -sin^2) =7(1-2sin^2x) = 7 -14sin^2x = 7sin^2x + 5

21sin^2x = 2

sin^2 = 2/21

sinx = + or - sqr(2/21)

x = about 18 degrees or 342 degrees or 188 degrees or 162 degrees

18/180 = 0.10 pi radians or 342/360 = 1.90 pi radians or 188/180 = 1.04 pi radians or 162/180 = .9 pi radians

0.1 pi radians =about 0.314 radians, 1.9 pi radians =about 5.97 radians, 1.04 pi radians = about 3.27 radians or .9 pi radians = 2.83 radians

x = pi/10 or 19pi/10 or 26pi/25 or 9pi/10

in order,

x = pi/10, 9pi/10, 26pi/25, 19pi/10

Answer 2

same as

7*(1-2sin²x)=7sin²x+5

sinx=+/-√(2/21)

for the plus option x = .31 radian and (π-.31) radian

for negative options must add 2π to answers to put in proper range for answer

so -.31 radian is sam as 2π-.31 radian

and (-π- -.3) same as -π+.31+2π=π+.31

.31, π-.31, π+.31, 2π-.31