(b) If \( \operatorname{cov} 18^{\circ} m p \), write the following in terme of \( p \) : \( \begin{array}{lllll}\text { (1) } \cos 198^{\circ} & \text { (2) } \sin 108^{\circ} & \text { (3) } \sin \left(-18^{\circ}\right) \\ \text { (4) } \tan 522^{\circ} & \text { (5) } \cos 36^{\circ} & \text { (6) } \sin 144^{\circ} \\ \text { (7) } \tan 216^{\circ} & \text { (8) } \cos 12^{\circ} & \text { (9) } & \sin 78^{\circ} \\ \text { (10) } 2 \cos ^{2} 9^{\circ} & \text { (11) } \sin ^{2} 9^{\circ} & \text { (12) } \sin 9^{\circ}\end{array} \)

To express the trigonometric functions in terms of \( p \) where \( p = \operatorname{cov} 18^{\circ} m \), we will use the following trigonometric identities and properties: 1. **Angle Reduction**: For angles greater than \( 360^{\circ} \) or less than \( 0^{\circ} \), we can reduce them by adding or subtracting \( 360^{\circ} \). 2. **Reference Angles**: For angles in different quadrants, we can use the reference angle to find the sine, cosine, and tangent values. 3. **Negative Angles**: The sine of a negative angle is the negative of the sine of the angle, and the cosine remains the same. Now, let's evaluate each expression step by step: 1. **(1) \( \cos 198^{\circ} \)**: \[ \cos 198^{\circ} = \cos(180^{\circ} + 18^{\circ}) = -\cos 18^{\circ} \] 2. **(2) \( \sin 108^{\circ} \)**: \[ \sin 108^{\circ} = \sin(90^{\circ} + 18^{\circ}) = \cos 18^{\circ} \] 3. **(3) \( \sin(-18^{\circ}) \)**: \[ \sin(-18^{\circ}) = -\sin 18^{\circ} \] 4. **(4) \( \tan 522^{\circ} \)**: \[ \tan 522^{\circ} = \tan(522^{\circ} - 360^{\circ}) = \tan 162^{\circ} = -\tan 18^{\circ} \] 5. **(5) \( \cos 36^{\circ} \)**: \[ \cos 36^{\circ} = \sin 54^{\circ} = \sin(90^{\circ} - 36^{\circ}) = \sin(90^{\circ} - 2 \times 18^{\circ}) = \sin 54^{\circ} \] 6. **(6) \( \sin 144^{\circ} \)**: \[ \sin 144^{\circ} = \sin(180^{\circ} - 36^{\circ}) = \sin 36^{\circ} \] 7. **(7) \( \tan 216^{\circ} \)**: \[ \tan 216^{\circ} = \tan(180^{\circ} + 36^{\circ}) = \tan 36^{\circ} \] 8. **(8) \( \cos 12^{\circ} \)**: \[ \cos 12^{\circ} = \cos(18^{\circ} - 6^{\circ}) \text{ (not simplified further without specific values)} \] 9. **(9) \( \sin 78^{\circ} \)**: \[ \sin 78^{\circ} = \sin(90^{\circ} - 12^{\circ}) = \cos 12^{\circ} \] 10. **(10) \( 2 \cos^{2} 9^{\circ} \)**: \[ 2 \cos^{2} 9^{\circ} = 1 + \cos 18^{\circ} \text{ (using the double angle formula)} \] 11. **(11) \( \sin^{2} 9^{\circ} \)**: \[ \sin^{2} 9^{\circ} = \frac{1 - \cos 18^{\circ}}{2} \text{ (using the half-angle formula)} \] 12. **(12) \( \sin 9^{\circ} \)**: \[ \sin 9^{\circ} \text{ (not simplified further without specific values)} \] Now, we can summarize the results in terms of \( p \): 1. \( -\cos 18^{\circ} \) 2. \( \cos 18^{\circ} \) 3. \( -\sin 18^{\circ} \) 4. \( -\tan 18^{\circ} \) 5. \( \cos 36^{\circ} \) 6. \( \sin 36^{\circ} \) 7. \( \tan 36^{\circ} \) 8. \( \cos 12^{\circ} \) 9. \( \cos 12^{\circ} \) 10. \( 1 + \cos 18^{\circ} \) 11. \( \frac{1 - \cos 18^{\circ}}{2} \) 12. \( \sin 9^{\circ} \) These expressions can be further evaluated if specific values for \( \cos 18^{\circ} \), \( \sin 18^{\circ} \), and \( \tan 18^{\circ} \) are provided.