SOLUTION: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x (Round each answer to four decimal places) 12

Algebra.Com
Question 847344: Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x (Round each answer to four decimal places)
12 sin^2 x − 17 sin x + 6 = 0
5 tan^2 x + 8 tan x − 4 = 0
tan^2 x + 4 tan x + 1 = 0
4 cos^2 x − 4 cos x − 1 = 0
4 tan^2 x + 21 tan x − 49 = 0
tan^2 x + 5 tan x + 2 = 0
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a graphing utility to approximate the angle x (Round each answer to four decimal places)
12sin^2(x) - 17sin(x) + 6 = 0 ************ don't put spaces after coefficients.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=1 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 0.75, 0.666666666666667. Here's your graph:

================================
sin(x) = 3/4
Use a calculator to find x
You can't get 4 decimal places on a graph.
----------------------
sin(x) = 2/3
============================================
do the others the same way.
5 tan^2 x + 8 tan x − 4 = 0
tan^2 x + 4 tan x + 1 = 0
4 cos^2 x − 4 cos x − 1 = 0
4 tan^2 x + 21 tan x − 49 = 0
tan^2 x + 5 tan x + 2 = 0
RELATED QUESTIONS

5sinx+2cosx=0 Use a graphing utility to approximate the solutions of the equation in the... (answered by Fombitz)
Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a... (answered by lwsshak3)
Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a... (answered by josmiceli)
Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a... (answered by ikleyn)
Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a... (answered by ikleyn)
Use the Quadratic Formula to solve the equation in the interval [0, 2π). Then use a... (answered by Alan3354)
Use the Quadratic Formula to solve the equation in the interval [0, 2𝜋). Then use a... (answered by MathLover1)
Use a graphing utility to approximate the solutions (to three decimal places) of the... (answered by Alan3354)
I have no idea how to start this problem. Ca you please help. Use a graphing utility to... (answered by Edwin McCravy)