Find the sine, cosine, and tangent of each angle using the unit circle.
$\(\theta\)=225\(\degree\),\(\left\)(-\(\frac{\sqrt2}{2}\),-\(\frac{\sqrt2}{2}\]\right\))$

• A. $\(\sin\]\theta\)=-\(\frac{\sqrt2}{2}\),\(\cos\[\theta\)=-\(\frac{\sqrt2}{2}\),\(\tan\]\theta\)=2$
• B. $\(\sin\]\theta\)=\(\frac{\sqrt2}{2}\),\(\cos\[\theta\)=-\(\frac{\sqrt2}{2}\),\(\tan\]\theta\)=-1$
• C. $\(\sin\]\theta\)=-\(\frac{\sqrt2}{2}\),\(\cos\[\theta\)=-\(\frac{\sqrt2}{2}\),\(\tan\]\theta\)=1$
• D. $\(\sin\]\theta\)=\(\frac{\sqrt2}{2}\),\(\cos\[\theta\)=\(\frac{\sqrt2}{2}\),\(\tan\]\theta\)=\(\frac{\sqrt2}{1}\)$

Answer: (C)

Verified step by step guidance

1. The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. Each point on the unit circle corresponds to an angle θ measured from the positive x-axis.
2. For an angle θ = 225°, locate the point on the unit circle. The coordinates of this point are given as (-\(\frac{\sqrt{2}\)}{2}, -\(\frac{\sqrt{2}\)}{2}).
3. The x-coordinate of the point on the unit circle represents the cosine of the angle, and the y-coordinate represents the sine of the angle. Therefore, \(\cos\)(225°) = -\(\frac{\sqrt{2}\)}{2} and \(\sin\)(225°) = -\(\frac{\sqrt{2}\)}{2}.
4. The tangent of an angle θ is the ratio of the sine to the cosine, \(\tan\)(θ) = \(\frac{\sin(θ)}{\cos(θ)}\). For θ = 225°, \(\tan\)(225°) = \(\frac{-\frac{\sqrt{2}\)}{2}}{-\(\frac{\sqrt{2}\)}{2}} = 1.
5. Verify the quadrant: 225° is in the third quadrant where both sine and cosine are negative, confirming that \(\sin\)(225°) = -\(\frac{\sqrt{2}\)}{2}, \(\cos\)(225°) = -\(\frac{\sqrt{2}\)}{2}, and \(\tan\)(225°) = 1 are correct.