Question

Using the unit circle, determine the value of tan(120°)

a) √3/3
b) -√3/3
c) -1
d) 1/√3

Answer 1

To determine the value of tan(120°) using the unit circle, we find the y-coordinate of the point on the unit circle corresponding to 120°, which gives us √3/2. We also find the x-coordinate, which gives us -1/2. Dividing the y-coordinate by the x-coordinate, we get -√3/3.

Step-by-step explanation:

To determine the value of tan(120°) using the unit circle, we need to find the y-coordinate of the point on the unit circle corresponding to 120°.

Since 120° is in the second quadrant, we know that the value of sin(120°) will be positive. Using the unit circle, we can see that sin(120°) is equal to √3/2.

Similarly, the value of cos(120°) in the second quadrant will be negative. Using the unit circle, we can see that cos(120°) is equal to -1/2.

Finally, tan(120°) is equal to sin(120°) / cos(120°), which simplifies to ( √3/2 ) / ( -1/2 ). Simplifying further, we get -√3/3.