Asked by lindsay
solve the equation: 4 tan^2 x + 12 sec x +1 =0, for 0 degrees is less than or equal to x is less than or equal to 360 degrees.
Answers
Answered by
Reiny
4 tan^2 x + 12 sec x +1 =0
4sin^2 x/cos^2 x + 12/cosx + 1 = 0
times cos^2 x
4sin^2x + 12cosx + cos^2x = 0
4(1-cos^2 x) + 12cosx + cos^2 x = 0
-3cos^2 x + 12cosx + 4 = 0
3cos^2 x - 12cosx - 4 = 0
cosx = (12 ± √192)/6
= 4.309.. which is not possible, or cosx = -.3094..
so x must be in quads II or III
x = 180-71.977° or x = 180+71.977
x = 108.02° or 251.98°
4sin^2 x/cos^2 x + 12/cosx + 1 = 0
times cos^2 x
4sin^2x + 12cosx + cos^2x = 0
4(1-cos^2 x) + 12cosx + cos^2 x = 0
-3cos^2 x + 12cosx + 4 = 0
3cos^2 x - 12cosx - 4 = 0
cosx = (12 ± √192)/6
= 4.309.. which is not possible, or cosx = -.3094..
so x must be in quads II or III
x = 180-71.977° or x = 180+71.977
x = 108.02° or 251.98°
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.