SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2𝜋). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list. R

Algebra ->  Trigonometry-basics -> SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2𝜋). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list. R      Log On


   

Question 1193896: Use the Quadratic Formula to solve the equation in the interval [0, 2𝜋). Then use a graphing utility to approximate the angle x. (Enter your answers as a comma-separated list. Round each answer to four decimal places.) (Four Answers)
6 tan^2 x + 35 tan x − 49 = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

you can use factoring instead of the Quadratic Formula to solve the equation

6tan%5E2%28+x%29+%2B+35tan+%28x%29+-49+=+0
let's tan+%28x%29=u
6u%5E2+%2B+35u+-49+=+0........factor
6u%5E2+%2B+42u-7u+-49+=+0
%286u%5E2+%2B+42u%29-%287u+%2B49%29+=+0
6u%28u+%2B+7%29-7%28u+%2B7%29+=+0
%28u+%2B+7%29+%286u+-+7%29+=+0........substitute back tan+%28x%29
%28tan+%28x%29+%2B+7%29+%286tan+%28x%29+-+7%29+=+0

solutions:
if %28tan+%28x%29+%2B+7%29++=+0 =>tan+%28x%29+=-+7 => x=tan%5E-1%28-7%29=> x=-tan%5E-1%287%29
if %286tan+%28x%29+-+7%29+=+0 =>6tan+%28x%29=+7=>tan+%28x%29=+7%2F6=>x=tan%5E-1%287%2F6%29

in the interval [0, 2pi), and since tan periodicity is+pi we have following
solutions:
x+=+pi-tan%5E-1%287%29=> x=1.7127
x+=+2pi-+tan%5E-1%287%29=>x=4.8543
x+=+pi%2B+tan%5E-1%287%2F6%29=>x=4.0038
x+=+2pi+-tan%5E-1%287%2F6%29=>x=5.4210

answer to four decimal places:1.7127,4.0038,4.8543,x=5.4210