Find one positive and one negative coterminal angle of each of the following. There is no need to graph the angles. $$ \begin{array}{llll} ext { A) } 30^{\circ} & ext { B) }-40^{\circ} & ext { C) } 150^{\circ} & ext { D) } 220^{\circ}\end{array} $$ $$ \begin{array}{llll} ext { E) }-330^{\circ} & ext { F) } \frac{\pi}{3} & ext { G) } \frac{5 \pi}{2} & ext { H) }-\frac{2 \pi}{3}\end{array} $$

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Find one positive and one negative coterminal angle of each of the following. There is no need to graph the angles. $$ \begin{array}{llll}	ext { A) } 30^{\circ} & 	ext { B) }-40^{\circ} & 	ext { C) } 150^{\circ} & 	ext { D) } 220^{\circ}\end{array} $$ $$ \begin{array}{llll}	ext { E) }-330^{\circ} & 	ext { F) } \frac{\pi}{3} & 	ext { G) } \frac{5 \pi}{2} & 	ext { H) }-\frac{2 \pi}{3}\end{array} $$

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Certainly! Coterminal angles are angles that share the same terminal side when positioned in standard form. To find coterminal angles, you can add or subtract full rotations:

- **In degrees**: Add or subtract $$360^\circ$$.
- **In radians**: Add or subtract $$2\pi$$.

Below are the positive and negative coterminal angles for each given angle:

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### **A) $$30^\circ$$**
- **Positive Coterminal Angle**: $$30^\circ + 360^\circ = 390^\circ$$
- **Negative Coterminal Angle**: $$30^\circ - 360^\circ = -330^\circ$$

### **B) $$-40^\circ$$**
- **Positive Coterminal Angle**: $$-40^\circ + 360^\circ = 320^\circ$$
- **Negative Coterminal Angle**: $$-40^\circ - 360^\circ = -400^\circ$$

### **C) $$150^\circ$$**
- **Positive Coterminal Angle**: $$150^\circ + 360^\circ = 510^\circ$$
- **Negative Coterminal Angle**: $$150^\circ - 360^\circ = -210^\circ$$

### **D) $$220^\circ$$**
- **Positive Coterminal Angle**: $$220^\circ + 360^\circ = 580^\circ$$
- **Negative Coterminal Angle**: $$220^\circ - 360^\circ = -140^\circ$$

### **E) $$-330^\circ$$**
- **Positive Coterminal Angle**: $$-330^\circ + 360^\circ = 30^\circ$$
- **Negative Coterminal Angle**: $$-330^\circ - 360^\circ = -690^\circ$$

### **F) $$\frac{\pi}{3}$$**
- **Positive Coterminal Angle**: $$\frac{\pi}{3} + 2\pi = \frac{7\pi}{3}$$
- **Negative Coterminal Angle**: $$\frac{\pi}{3} - 2\pi = -\frac{5\pi}{3}$$

### **G) $$\frac{5\pi}{2}$$**
- **Positive Coterminal Angle**: $$\frac{5\pi}{2} + 2\pi = \frac{9\pi}{2}$$
- **Negative Coterminal Angle**: $$\frac{5\pi}{2} - 4\pi = -\frac{3\pi}{2}$$

### **H) $$-\frac{2\pi}{3}$$**
- **Positive Coterminal Angle**: $$-\frac{2\pi}{3} + 2\pi = \frac{4\pi}{3}$$
- **Negative Coterminal Angle**: $$-\frac{2\pi}{3} - 2\pi = -\frac{8\pi}{3}$$

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Feel free to choose any other multiples of full rotations ($$360^\circ$$ or $$2\pi$$) to find additional coterminal angles as needed.
Here are the positive and negative coterminal angles for each given angle: - **A) $$30^\circ$$:** - Positive: $$390^\circ$$ - Negative: $$-330^\circ$$ - **B) $$-40^\circ$$:** - Positive: $$320^\circ$$ - Negative: $$-400^\circ$$ - **C) $$150^\circ$$:** - Positive: $$510^\circ$$ - Negative: $$-210^\circ$$ - **D) $$220^\circ$$:** - Positive: $$580^\circ$$ - Negative: $$-140^\circ$$ - **E) $$-330^\circ$$:** - Positive: $$30^\circ$$ - Negative: $$-690^\circ$$ - **F) $$\frac{\pi}{3}$$:** - Positive: $$\frac{7\pi}{3}$$ - Negative: $$-\frac{5\pi}{3}$$ - **G) $$\frac{5\pi}{2}$$:** - Positive: $$\frac{9\pi}{2}$$ - Negative: $$-\frac{3\pi}{2}$$ - **H) $$-\frac{2\pi}{3}$$:** - Positive: $$\frac{4\pi}{3}$$ - Negative: $$-\frac{8\pi}{3}$$

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