Question

I need help with this practice problem It’s from my trigonometry prep guide

Answer 1

Reference angles

1.

`\begin{gathered} -(23\pi)/(6)\cdot(180)/(\pi)=-690 \\ -690+720=30\text{ is in Q1} \\ \theta_(ref)=30 \\ 30\cdot(\pi)/(180)=(\pi)/(6) \end{gathered}`

`\theta=-(23\pi)/(6)\rightarrow\theta_(ref)=(\pi)/(6)`

2.

`\begin{gathered} (7)/(5)\pi\cdot(180)/(\pi)=252 \\ 252\text{ is in Q}3 \\ \theta_(ref)=252-180=72 \\ 72\cdot(\pi)/(180)=(2)/(5)\pi \end{gathered}`
`\theta=(7)/(5)\pi\rightarrow\theta_(ref)=(2)/(5)\pi`

3.

`\begin{gathered} -(11\pi)/(12)\cdot(180)/(\pi)=-165 \\ -165+360=195 \\ 195\text{ is in Q3} \\ \theta_(ref)=195-180=15 \\ 15\cdot(\pi)/(180)=(\pi)/(12) \end{gathered}`
`\theta=-(11\pi)/(12)\rightarrow\theta_(ref)=(\pi)/(12)`