Choose all of the equations below that have only one solution for $$ x $$ when $$ 0^{\circ} \leq x \leq 360^{\circ} $$ $$ \begin{array}{llll}\sin x=-1 & \sin x=0 & \sin x=0.5 & \sin x=1 \ \cos x=-1 & \cos x=0 & \cos x=0.5 & \cos x=1\end{array} $$

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To determine which equations have only one solution for $$ x $$ in the interval $$ 0^{\circ} \leq x \leq 360^{\circ} $$, we will analyze each equation one by one.

1. **$$\sin x = -1$$**:
   - The sine function equals -1 at $$ x = 270^{\circ} $$.
   - **Number of solutions: 1**

2. **$$\sin x = 0$$**:
   - The sine function equals 0 at $$ x = 0^{\circ}, 180^{\circ}, 360^{\circ} $$.
   - **Number of solutions: 3**

3. **$$\sin x = 0.5$$**:
   - The sine function equals 0.5 at $$ x = 30^{\circ} $$ and $$ x = 150^{\circ} $$.
   - **Number of solutions: 2**

4. **$$\sin x = 1$$**:
   - The sine function equals 1 at $$ x = 90^{\circ} $$.
   - **Number of solutions: 1**

5. **$$\cos x = -1$$**:
   - The cosine function equals -1 at $$ x = 180^{\circ} $$.
   - **Number of solutions: 1**

6. **$$\cos x = 0$$**:
   - The cosine function equals 0 at $$ x = 90^{\circ} $$ and $$ x = 270^{\circ} $$.
   - **Number of solutions: 2**

7. **$$\cos x = 0.5$$**:
   - The cosine function equals 0.5 at $$ x = 60^{\circ} $$ and $$ x = 300^{\circ} $$.
   - **Number of solutions: 2**

8. **$$\cos x = 1$$**:
   - The cosine function equals 1 at $$ x = 0^{\circ} $$ and $$ x = 360^{\circ} $$.
   - **Number of solutions: 2**

From this analysis, the equations that have only one solution for $$ x $$ in the interval $$ 0^{\circ} \leq x \leq 360^{\circ} $$ are:

- $$\sin x = -1$$
- $$\sin x = 1$$
- $$\cos x = -1$$

Thus, the equations with only one solution are:

$$
\sin x = -1, \quad \sin x = 1, \quad \cos x = -1
$$
The equations with only one solution are: $$\sin x = -1$$, $$\sin x = 1$$, $$\cos x = -1$$.

Choose all of the equations below that have only one solution for \( x \) when \[ 0^{\circ} \leq x \leq 360^{\circ} \] \[ \begin{array}{llll}\sin x=-1 & \sin x=0 & \sin x=0.5 & \sin x=1 \\ \cos x=-1 & \cos x=0 & \cos x=0.5 & \cos x=1\end{array} \]

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