Question

Use the Quadratic Formula to solve the equation in the interval
[0, 2π).
Then use a graphing utility to approximate the angle x. (Round your answers to four decimal places.)
4 tan^2 x + 9 tan x − 9 = 0
x = (smallest value)
x =
x =
x = (largest value)

Answer 1

and what is the quadratic formula?

Answer 2

ax^2+bx+c=0

Answer 3

given the format: ax^2 + bx + c = 0

we can derive the quadratic formula, or simply remember it :)

\[x = \frac{1}{2a}(-b\pm\sqrt{b^2-4ac})\]

Answer 4

in this case, we can substitute x, with tan(x) and the rest is the same

a = 4, b=9, and c = -9

plug and play

Answer 5

ok, so i get

Answer 6

(-9+-√-63))/8

Answer 7

check your b^2 - 4ac part

81 -4(4*-9) will be positive

Answer 8

sqrt(225) = 15

(-9+-15)/8 is what i get

Answer 9

oh yes, you're right

Answer 10

after that we have to play with trig :)

Answer 11

ok, this where i get lost a little with what i am trying to answer.

Answer 12

tan(x) = -24/8 = -3/1

tan(x) = 16/8 = 2

each of those values have 2 angles each that match it

Answer 13

where are you getting those?

Answer 14

i figured id use what we found from the quad formula and apply it to solving for tan(x) ...

(-9+-15)/8: (-9-15)/8 and (-9+15)/8

Answer 15

hmmmm, but without the errors :)

Answer 16

ohhh i see now. ok go on.

Answer 17

simplify those and the rest is trig-y

tan(x) = -3

tan(x) = 3/4

use arctan to find one angle for each one, then add pi to get the other value