Question

HELP PLEASE WITH NUMBER 4. I'LL GIVE YOU FULL 50 POINTS WITH STEP BY STEP WORKING!!!

Answer 1

A)

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\boxed{\dfrac{a}{b}}$

b)

From the reduction formulas we know that:

$\sin(\pi-\theta)=\sin(\theta)=\boxed{a}$

c)

$\cos(\pi+\theta)=-\cos(\theta)=\boxed{-b}$

d)

$\tan(\pi+\theta)=\dfrac{\sin(\pi+\theta)}{\cos(\pi+\theta)}=\dfrac{-\sin(\theta)}{-\cos(\theta)}=\dfrac{\sin(\theta)}{\cos(\theta)}=\boxed{\dfrac{a}{b}}$

e)

$\sin(\pi+\theta)=-\sin(\theta)=\boxed{-a}$

f)

Cosine is an even function, so:

$\cos(-\theta)=\cos(\theta)=\boxed{b}$

g)

$\sin(2\pi-\theta)=-\sin(\theta)=\boxed{-a}$

h)

$\cos(\theta-\pi)=\cos\big(-(\pi-\theta)\big)=\cos(\pi-\theta)=-\cos(\theta)=\boxed{-b}$