Answer:
A
Step-by-step explanation:
Remember that tangent is the ratio of sine over cosine.
[tex]\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}[/tex]
In the unit circle:
- Sine refers to the y-coordinate.
- Cosine refers to the x-coordinate.
Our x-coordinate is -√2/2 and our y-coordinate is √2/2.
So, substitute -√2/2 for cosine and √2/2 for sine. This yields:
[tex]\tan(\theta)=\frac{\sqrt2/2}{-\sqrt2/2}[/tex]
Since the numerator and the denominator are the same save for a negative, we can cancel them:
[tex]\tan(\theta)=-1[/tex]
So, our answer is A.
