trig quiz\n0:40:08 rem\nprevious page next page\nquestion 34 (1 point)\nwhich set of primary trigonometric…

trig quiz\n0:40:08 rem\nprevious page next page\nquestion 34 (1 point)\nwhich set of primary trigonometric ratios is correct for the angle 225°?\no a)\n( sin 225^{circ}=-\frac{1}{sqrt{2}}, cos 225^{circ}=-\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=1 )\no b)\n( sin 225^{circ}=-\frac{1}{sqrt{2}}, cos 225^{circ}=\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=-1 )\no c)\n( sin 225^{circ}=\frac{1}{sqrt{2}}, cos 225^{circ}=-\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=1 )\no d)\n( sin 225^{circ}=\frac{1}{sqrt{2}}, cos 225^{circ}=\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=-1 )\nprevious page next page\npage\nsubmit quiz 33 of 35 questions saved

trig quiz\n0:40:08 rem\nprevious page next page\nquestion 34 (1 point)\nwhich set of primary trigonometric ratios is correct for the angle 225°?\no a)\n( sin 225^{circ}=-\frac{1}{sqrt{2}}, cos 225^{circ}=-\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=1 )\no b)\n( sin 225^{circ}=-\frac{1}{sqrt{2}}, cos 225^{circ}=\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=-1 )\no c)\n( sin 225^{circ}=\frac{1}{sqrt{2}}, cos 225^{circ}=-\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=1 )\no d)\n( sin 225^{circ}=\frac{1}{sqrt{2}}, cos 225^{circ}=\frac{1}{sqrt{2}} ),\n( \tan 225^{circ}=-1 )\nprevious page next page\npage\nsubmit quiz 33 of 35 questions saved

Answer

Explanation:

Step1: Determine the reference angle

The angle (225^{\circ}) is in the third quadrant. The reference angle (\theta_{r}=225^{\circ}- 180^{\circ}=45^{\circ}). In the third quadrant, (\sin\theta<0), (\cos\theta<0), and (\tan\theta>0).

Step2: Calculate the trigonometric ratios

We know that (\sin45^{\circ}=\frac{1}{\sqrt{2}}), (\cos45^{\circ}=\frac{1}{\sqrt{2}}), and (\tan45^{\circ} = 1). Since (\sin225^{\circ}=-\sin45^{\circ}=-\frac{1}{\sqrt{2}}), (\cos225^{\circ}=-\cos45^{\circ}=-\frac{1}{\sqrt{2}}), and (\tan225^{\circ}=\tan45^{\circ} = 1)

Answer:

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