Question 441508: Use the Quadratic Formula to solve the equation in the interval
[0, 2π). (Round your answers to four decimal places.)
4 tan2 x + 15 tan x − 25 = 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Use the Quadratic Formula to solve the equation in the interval
[0, 2π). (Round your answers to four decimal places.)
4 tan2 x + 15 tan x − 25 = 0
..
I will assume the first term is 4 tan^2x instead of 4 tanx as given
4 tan^2 x + 15 tan x − 25 = 0
a=4, b=15, c=-25
tanx=[-15+-sqrt(15^2-4*4*-25)]/2*4
=[-15+-sqrt(625)]/8
=(-15+-25)/8
=-40/8 or 10/8
=-5 or 1.25
using inverse function key for tan
tanx=-5
x=101.3099º (note that calculator will give a reference angle of -78.6900º, but this is not within specified domain for x, hence the angle must be in quadrant II where tan x is also negative)
tanx=1.25
x=51.3402º
ans:
x=101.3099º and 51.3402º in domain[0,2π)
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