a)
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\boxed{\dfrac{a}{b}} [/tex]
b)
From the reduction formulas we know that:
[tex]\sin(\pi-\theta)=\sin(\theta)=\boxed{a} [/tex]
c)
[tex]\cos(\pi+\theta)=-\cos(\theta)=\boxed{-b}[/tex]
d)
[tex]\tan(\pi+\theta)=\dfrac{\sin(\pi+\theta)}{\cos(\pi+\theta)}=\dfrac{-\sin(\theta)}{-\cos(\theta)}=\dfrac{\sin(\theta)}{\cos(\theta)}=\boxed{\dfrac{a}{b}}[/tex]
e)
[tex]\sin(\pi+\theta)=-\sin(\theta)=\boxed{-a}[/tex]
f)
Cosine is an even function, so:
[tex]\cos(-\theta)=\cos(\theta)=\boxed{b}[/tex]
g)
[tex]\sin(2\pi-\theta)=-\sin(\theta)=\boxed{-a} [/tex]
h)
[tex]\cos(\theta-\pi)=\cos\big(-(\pi-\theta)\big)=\cos(\pi-\theta)=-\cos(\theta)=\boxed{-b} [/tex]
