How do you use a graphing utility to approximate the solutions of $csc^2x+0.5cotx-5=0$ in the interval $[0,2pi)$ ?

Question

2599 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-20T14:59:27

0.56, 2.56, 3.15, 5.70 and 6.24.

The period for the function is $2pi$ .

The general solutions are

$x = 2kpi$ + a soluion in the list, $k = +-1, +-2, +-3, ...$

The first graph gives locations. The other graphs narrow down to

near-linearity, near the solutions.

These approximations can be used as starters, for numerical

iterative methods that would generate quite many correct significant

digits (sd), in the solutions,

graph{2+sin x (cos x-5sin x) [-10, `10. -.5, .5]}

graph{2+sin x (cos x-5sin x) [0.55 0.56 -3.14, 3.14]}

graph{2+sin x (cos x-5sin x) [2.5, 2.6 -3.14, 3.14]}

graph{2+sin x (cos x-5sin x) [3.1, 3.2 -3.14, 3.14]}

graph{2+sin x (cos x-5sin x) [5.7 5.71, -3.14, 3.14]}

graph{2+sin x (cos x-5sin x) [6.23, 6.26 -3.14, 3.14]}

How do you use a graphing utility to approximate the solutions of csc^2x+0.5cotx-5=0csc^2x+0.5cotx-5=0 in the interval [0,2pi)[0,2pi)?