find all the solutions to the equation in the intercal [0,2pi) using the equation:
sec^2x+5tanx=-2

Question

find all the solutions to the equation in the intercal [0,2pi) using the equation: 
sec^2x+5tanx=-2

anonymous · Answer

sec^2x = 1 + tan^2x
so
 tan^2x + 5 tanx + 3 = 0

solving this give tan x = -0.6972  or -4.302
values for x are 2.53, 5.67, 1.8, 4.94 radians
if you require answers is degrees multiply the above by  180/pi

anonymous · Answer

ok so i can get to the tan^2 + 5tanx = 0 but how do you actually get to the answers?

anonymous · Answer

you can solve that quadratic using the formula.
find the angles by plugging  tan-1   0.6972 and  4.302 into your calculator
this gives angles in first quadrant  -  then work out angles corresponding to negatives
- tangents are negative in the second and fourth quadrants

anonymous · Answer

isnt ther something that you can do with it by factoring the left side of tan^2x+5tanx+3=0? and then you set them equal to 0 and solve?

anonymous · Answer

hey I have one more question how do u get the values of x?