# Trigonometric inequality problem.

1. Aug 31, 2011

### Michael_Light

1. The problem statement, all variables and given/known data

Deduce that 0 ≤ ≤ 10/9 for all values of x.

2. Relevant equations

3. The attempt at a solution

Is it possible to sketch a graph for ? How?

Or is there any methods to find the max./min. value of ?

2. Aug 31, 2011

### lanedance

is the denominator ever zero or negative? if not try mutiplying through by it

or find the critical points to fiind max and min

3. Sep 1, 2011

4. Sep 1, 2011

### Pi-Bond

If you can prove $1+sin(x)-\frac{10}{9}(5+4cos(x))$ is always less than 0, you can get the less than part. If you think about the numerator, the greater than part also follows quickly.