question 23 (1 point) which set of primary trigonometric ratios is correct for the angle 225°? a) sin 225° =…

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

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

Answer

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)