Question

Please help!
maths trig functions

Answer 1

1. According to the plot, this happens twice for some
`x` between 135° and 180°, and for some
`x` between 270° and 315°.

We could try finding them exactly, but we would end up having to solve a 4th degree polynomial equation that doesn't factorize nicely...

2. Rewrite the inequality as

`3\sin(x) - 2 > \tan(x) \implies 3 \sin(x) > \tan(x) + 2`

The curve
`y=3\sin(x)` lies above
`y=\tan(x)+2` when
`90^\circ < x < \alpha`, where
`\alpha` is the first solution mentioned in (1) between 135° and 180°, approximately
`\alpha\approx151.127^\circ`.

3. Rewriting

`\tan(x) \ge 1 \implies \tan(x) + 2 \ge 3`

we see from the plot that this is true for
`x` between 45° and 90°, and again between 225° and 270°.