Trigonometric inequality problem.

[Michael_Light]

Homework Statement

Deduce that 0 ≤

≤ 10/9 for all values of x.

Homework Equations

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

?

Please enlighten me...

 

[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

 

[NascentOxygen]

http://fooplot.com/index.php?q0=(1+sin(x))/(5+4*cos(x))

 

[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.