Question

coterminal angles
determine the first three positive angles and the first three negative angles that are coterminal with 46°.
give your answers as expressions and allow amplify to show the final answer. use the previous answers for the subsequent answers in both sets.
positive (1 rotation)
positive (2 rotations)

Explanation:

Step1: Recall coterminal - angle formula

Coterminal angles of an angle $\theta$ are given by $\theta + 360^{\circ}n$, where $n$ is an integer.

Step2: Find first - positive coterminal angle (1 rotation)

For $n = 1$ and $\theta=46^{\circ}$, the angle is $46^{\circ}+360^{\circ}\times1 = 406^{\circ}$.

Step3: Find second - positive coterminal angle (2 rotations)

For $n = 2$ and $\theta = 46^{\circ}$, the angle is $46^{\circ}+360^{\circ}\times2=46^{\circ}+720^{\circ}=766^{\circ}$.

Step4: Find third - positive coterminal angle (3 rotations)

For $n = 3$ and $\theta = 46^{\circ}$, the angle is $46^{\circ}+360^{\circ}\times3=46^{\circ}+1080^{\circ}=1126^{\circ}$.

Step5: Find first - negative coterminal angle

For $n=-1$ and $\theta = 46^{\circ}$, the angle is $46^{\circ}+360^{\circ}\times(-1)=46^{\circ}-360^{\circ}=-314^{\circ}$.

Step6: Find second - negative coterminal angle

For $n = - 2$ and $\theta = 46^{\circ}$, the angle is $46^{\circ}+360^{\circ}\times(-2)=46^{\circ}-720^{\circ}=-674^{\circ}$.

Step7: Find third - negative coterminal angle

For $n=-3$ and $\theta = 46^{\circ}$, the angle is $46^{\circ}+360^{\circ}\times(-3)=46^{\circ}-1080^{\circ}=-1034^{\circ}$.

Answer:

Positive (1 Rotation): $406^{\circ}$
Positive (2 Rotations): $766^{\circ}$
Positive (3 Rotations): $1126^{\circ}$
Negative (1 Rotation): $-314^{\circ}$
Negative (2 Rotations): $-674^{\circ}$
Negative (3 Rotations): $-1034^{\circ}$