Recall that
[tex]\sin^2\phi+\cos^2\phi=1\implies\tan^2\phi+1=\sec^2\phi[/tex]
Then with [tex]\tan\phi=\dfrac34[/tex], we have
[tex]\sec^2\phi=\dfrac9{16}+1=\dfrac{25}{16}\implies\sec\phi=\pm\dfrac54\implies\cos\phi=\pm\dfrac45[/tex]
Since
[tex]\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac{\sin\phi}{\pm\frac45}=\dfrac34[/tex]
it follows that
[tex]\sin\phi=\pm\dfrac35[/tex]
So,
[tex]3\sin\phi+2\cos\phi=\pm\dfrac95\pm\dfrac85=\pm\dfrac{17}5[/tex]
