QuestionL steps for full marks as required. Correct answer with NO work shown = NO ma
1. Determine the exact values of the six trigonometric ratios for $585^{\circ}$. [8.1] [2 marks]

Studdy Solution
Calculate the remaining trigonometric ratios:
- $\tan(225^\circ) = \frac{\sin(225^\circ)}{\cos(225^\circ)} = \frac{-\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = 1$ - $\csc(225^\circ) = \frac{1}{\sin(225^\circ)} = -\sqrt{2}$ - $\sec(225^\circ) = \frac{1}{\cos(225^\circ)} = -\sqrt{2}$ - $\cot(225^\circ) = \frac{1}{\tan(225^\circ)} = 1$
The exact values of the six trigonometric ratios for $585^\circ$ are:
$\sin(585^\circ) = -\frac{\sqrt{2}}{2}, \quad \cos(585^\circ) = -\frac{\sqrt{2}}{2}, \quad \tan(585^\circ) = 1$
$\csc(585^\circ) = -\sqrt{2}, \quad \sec(585^\circ) = -\sqrt{2}, \quad \cot(585^\circ) = 1$