How to do it on calculator

The best way to do math on a calculator is to turn it over and use it as a backboard for your writing. :)

I thin you need to check what you wrote. Is it 4 \cos \theta +5 \sin \theta or is it 4\cos \theta \cdot 5 \sin \theta =6 ? If it's the second one use the identity 2\cos \theta \sin \theta = sin 2\theta and the solution falls out of the bottom. If it's the first one, that can be rough, when I solved it I needed the quadratic formula and the identity \cos^2 +sin^2 =1 , so I can can see your difficulty. If it's the first one, give me an honest effort and show me what you've done and I'll show you how to do it.