(b) If \( \sin 10^{\circ}=m \), write the following in terms of \( m \) : (1) \( \sin 350^{\circ} \) (2) \( \sin \left(-10^{\circ}\right) \) (3) \( \cos 260^{\circ} \) (4) \( \cos 10^{\circ} \) (5) \( \tan 170^{\circ} \)

To express these trigonometric functions in terms of \( m = \sin 10^\circ \), let's utilize trigonometric identities and properties of the sine and cosine functions. 1. \( \sin 350^{\circ} = \sin (360^{\circ} - 10^{\circ}) = -\sin 10^{\circ} = -m \) 2. \( \sin (-10^{\circ}) = -\sin 10^{\circ} = -m \) 3. \( \cos 260^{\circ} = \cos(270^{\circ} - 10^{\circ}) = -\sin 10^{\circ} = -m \) 4. \( \cos 10^{\circ} = \sqrt{1 - \sin^2 10^{\circ}} = \sqrt{1 - m^2} \) 5. \( \tan 170^{\circ} = \frac{\sin 170^{\circ}}{\cos 170^{\circ}} = \frac{\sin (180^{\circ} - 10^{\circ})}{-\cos(180^{\circ} - 10^{\circ})} = \frac{\sin 10^{\circ}}{-\cos 10^{\circ}} = -\frac{m}{\sqrt{1 - m^2}} \) So the answers are: 1) \( -m \) 2) \( -m \) 3) \( -m \) 4) \( \sqrt{1 - m^2} \) 5) \( -\frac{m}{\sqrt{1 - m^2}} \)