Question

trig quiz
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question 34 (1 point)
which set of primary trigonometric ratios is correct for the angle 225°?
o a)
( sin 225^{circ}=-\frac{1}{sqrt{2}}, cos 225^{circ}=-\frac{1}{sqrt{2}} ),
( \tan 225^{circ}=1 )
o b)
( sin 225^{circ}=-\frac{1}{sqrt{2}}, cos 225^{circ}=\frac{1}{sqrt{2}} ),
( \tan 225^{circ}=-1 )
o c)
( sin 225^{circ}=\frac{1}{sqrt{2}}, cos 225^{circ}=-\frac{1}{sqrt{2}} ),
( \tan 225^{circ}=1 )
o d)
( sin 225^{circ}=\frac{1}{sqrt{2}}, cos 225^{circ}=\frac{1}{sqrt{2}} ),
( \tan 225^{circ}=-1 )
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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. \(\sin225^{\circ}=-\frac{1}{\sqrt{2}}\), \(\cos225^{\circ}=-\frac{1}{\sqrt{2}}\), \(\tan225^{\circ}=1\)