Question

I need help with this practice problem It’s asks to Drag the angle measure to each box to match the quadrant location of the terminal ray of the angle op

Answer 1

Note that the range in quadrants are :

`\begin{gathered} Q1\colon\text{From}\quad 0\pi-0.5\pi \\ Q2\colon\text{From}\quad 0.5\pi-1.0\pi \\ Q3\colon\text{From}\quad 1.0\pi-1.5\pi \\ Q4\colon\text{From}\quad 1.5\pi-2\pi \end{gathered}`

From the problem,

`\begin{gathered} (3\pi)/(4)=0.75\pi\Rightarrow Q2 \\ (57\pi)/(8)=7.125\pi \\ \text{Note that 1 whole circle is}\quad 2\pi \\ \text{Subtracting three}\quad 2\pi \\ 7.125\pi-3(2\pi)=1.125\pi \\ \text{and}\quad 1.125\pi\quad \text{ is at Q3} \\ \\ (13\pi)/(6)=2.167\pi \\ Subtract\quad 2\pi \\ 2.167\pi-2\pi=0.167\pi\Rightarrow Q1 \end{gathered}`

The first three answers are :

Q2, Q3 and Q1

For the second set, we have negative angles.

The range of negative angles will be the reversal of the positive angles.

This will be :

`\begin{gathered} Q1\colon\text{From}\quad -1.5\pi\quad to\quad -2\pi \\ Q2\colon\text{From}\quad -1.0\pi\quad to\quad -1.5\pi \\ Q3\colon\text{From}\quad -0.5\pi\quad to\quad -1.0\pi \\ Q4\colon\text{From}\quad -0\pi\quad to\quad -0.5\pi \end{gathered}`

The following angles are :

`\begin{gathered} -(35\pi)/(4)=-8.75\pi \\ \text{Add four}\quad 2\pi \\ -8.75+4(2\pi)=-0.75\pi \\ -0.75\pi\Rightarrow Q3 \\ \\ -(5\pi)/(6)=-0.83\pi\Rightarrow Q3 \\ \\ -(5\pi)/(11)=-0.45\pi\Rightarrow Q4 \end{gathered}`

The last three answers are :

Q3, Q3 and Q4

To summarized :

`\begin{gathered} Q1\colon(13\pi)/(6) \\ Q2\colon(3\pi)/(4) \\ Q3\colon(57\pi)/(8),\quad -(35\pi)/(4),\quad -(5\pi)/(6) \\ Q4\colon-(5\pi)/(11) \end{gathered}`