8 Draw a diagram for each question. 8.1 If \( \tan 28^{\circ}=p \), write down the following in terms of \( p \). 8.1.1 \( \tan 152^{\circ} \) 8.1.2 \( \cos \left(-28^{\circ}\right) \) \( 8.1 .3 \sin 62^{\circ} \) 8.2 If \( 2 \sin 41^{\circ}=a \), write down the following in terms of \( a \). \( 8.2 .1 \sin 319^{\circ} \) 8. \( 2.2 \cos 49^{\circ} \) 8.2.3 \( \cos 139^{\circ} \)

To tackle these trigonometry questions, it's essential to recall some key angle identities and properties of the sine and cosine functions as well as how tangent behaves with reference to complementary and supplementary angles. First additional information: When finding \( \tan 152^{\circ} \), you can use the identity \( \tan(180^{\circ} - x) = -\tan(x) \). Thus, \( \tan 152^{\circ} = \tan(180^{\circ} - 28^{\circ}) = -\tan(28^{\circ}) = -p \). For \( \cos(-28^{\circ}) \), remember that cosine is an even function, so \( \cos(-28^{\circ}) = \cos(28^{\circ}) \), which can be expressed in terms of \( p \) using \( \cos^2(28^{\circ}) + \sin^2(28^{\circ}) = 1 \). Second additional information: For \( \sin 62^{\circ} \), you can use the complementary angle identity \( \sin(90^{\circ} - x) = \cos(x) \). Thus, \( \sin(62^{\circ}) = \sin(90^{\circ} - 28^{\circ}) = \cos(28^{\circ}) \), which can also be derived from the previous discussion involving \( p \). As for the second part, using \( 2 \sin 41^{\circ} = a \), you find \( \sin 319^{\circ} \) by noting \( 319^{\circ} = 360^{\circ} - 41^{\circ} = -\sin(41^{\circ}) \), hence \( \sin 319^{\circ} = -\sin(41^{\circ}) = -\frac{a}{2} \).