Question

question 23 (1 point) which set of primary trigonometric ratios is correct for the angle 225°? a) sin 225° = 1/√2, cos 225° = 1/√2, tan 225° = -1 b) sin 225° = -1/√2, cos 225° = 1/√2, tan 225° = -1 c) sin 225° = 1/√2, cos 225° = -1/√2, tan 225° = 1 d) sin 225° = -1/√2, cos 225° = -1/√2, tan 225° = 1

Explanation:

Step1: Determine the quadrant

\(225^{\circ}=180^{\circ} + 45^{\circ}\), so the angle \(225^{\circ}\) is in the third quadrant. In the third quadrant, \(\sin\theta<0\), \(\cos\theta<0\), and \(\tan\theta=\frac{\sin\theta}{\cos\theta}>0\).

Step2: Use the reference - angle formula

The reference angle \(\theta_{r}=225^{\circ}-180^{\circ} = 45^{\circ}\).
We know that \(\sin45^{\circ}=\frac{1}{\sqrt{2}}\), \(\cos45^{\circ}=\frac{1}{\sqrt{2}}\), and \(\tan45^{\circ}=1\).
Since \(\sin225^{\circ}=-\sin45^{\circ}\), \(\cos225^{\circ}=-\cos45^{\circ}\), and \(\tan225^{\circ}=\tan45^{\circ}\) (because \(\tan\theta\) is positive in the third quadrant).
So \(\sin225^{\circ}=-\frac{1}{\sqrt{2}}\), \(\cos225^{\circ}=-\frac{1}{\sqrt{2}}\), \(\tan225^{\circ}=1\)

Answer:

d) \(\sin225^{\circ}=-\frac{1}{\sqrt{2}}\), \(\cos225^{\circ}=-\frac{1}{\sqrt{2}}\), \(\tan225^{\circ}=1\)