Show ALL work and \begin{tabular}{|l} **\#1.) Which angle is not coterminal with $$ 130^{\circ} $$ ? \ a) $$ -590^{\circ} $$ \ b) $$ -230^{\circ} $$ \ c) $$ -130^{\circ} $$ \ d) $$ 490^{\circ} $$\end{tabular}

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UpStudy AI · Accepted Answer

**Step 1.** Two angles are coterminal if they differ by a multiple of $$360^\circ$$. That is, angles $$\theta$$ and $$\theta + 360k$$ (where $$k$$ is an integer) are coterminal.

**Step 2.** Check each option:

- **Option a: $$-590^\circ$$**
  
  Add $$720^\circ$$ (i.e., $$2 \times 360^\circ$$) to $$-590^\circ$$:
  
  $$
  -590^\circ + 720^\circ = 130^\circ
  $$
  
  So, $$-590^\circ$$ is coterminal with $$130^\circ$$.

- **Option b: $$-230^\circ$$**
  
  Add $$360^\circ$$ to $$-230^\circ$$:
  
  $$
  -230^\circ + 360^\circ = 130^\circ
  $$
  
  So, $$-230^\circ$$ is coterminal with $$130^\circ$$.

- **Option c: $$-130^\circ$$**
  
  Add $$360^\circ$$ to $$-130^\circ$$:
  
  $$
  -130^\circ + 360^\circ = 230^\circ
  $$
  
  Since $$230^\circ \ne 130^\circ$$, $$-130^\circ$$ is not coterminal with $$130^\circ$$.

- **Option d: $$490^\circ$$**
  
  Subtract $$360^\circ$$ from $$490^\circ$$:
  
  $$
  490^\circ - 360^\circ = 130^\circ
  $$
  
  So, $$490^\circ$$ is coterminal with $$130^\circ$$.

**Conclusion:** The angle that is not coterminal with $$130^\circ$$ is $$-130^\circ$$.
The angle that is not coterminal with $$130^\circ$$ is $$-130^\circ$$.

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**#1.) Which angle is not coterminal with ?

a)

b)

c)

d)

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