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.

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.      Log On


   

Question 856566: 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.)
1. 4cosine^2 x - 4cosine x - 1=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The unknown is +cos%28x%29+
I could say:
+z+=+cos%28x%29+
+4z%5E2+-+4z+-+1+=+0+
Here's the graph:
+graph%28+400%2C+400%2C+-4%2C+4%2C+-4%2C+4%2C+4x%5E2+-+4x+-+1+%29+
Now I can zero in:
+graph%28+400%2C+400%2C+-.5%2C+0%2C+-.5%2C+.5%2C+4x%5E2+-+4x+-+1+%29+
This is between +z+=+-.5+ and +z+=+0+
It looks like +z+=+-.2+
and the other zero crossing:
+graph%28+400%2C+400%2C+1%2C+1.5%2C+-.5%2C+.5%2C+4x%5E2+-+4x+-+1+%29+
This is between +z+=+1+ and +z+=+1.5+
It looks like +z+=+1.2+
This is invalid since the
cosine can't exceed +1+
----------------------
+-.2+=+cos%28x%29+
+x+=+1.7722+ radians
check:
+4z%5E2+-+4z+-+1+=+0+
+4%2Acos%5E2%28x%29+-+4%2Acos%28x%29+-+1+=+0+
+4%2A.04002+-+4%2A%28-.20004+%29+-+1+=+0+
+.16002+%2B+.80004+-+1+=+0+
+.960024+=+1+
pretty close
Hope I got it