Use the unit​ circle, along with the definitions of the circular​ functions, to find the exact value for the function at the​ right, given s = π/3. (Hint: The function on the right is tan π/3.)

Answer 1

To find the exact value of the function tan(π/3), we can use the reference angle of π/3 in the unit circle.

Starting from the positive x-axis, we move in a counterclockwise direction by π/3 radians. This brings us to the point (cos(π/3), sin(π/3)) on the unit circle.

Using the values of sin and cos for π/3, we have:

sin(π/3) = √3/2
cos(π/3) = 1/2

Now, we can use the definition of tan(x) = sin(x)/cos(x) to find the value of tan(π/3):

tan(π/3) = sin(π/3)/cos(π/3)
= (√3/2) / (1/2)
= (√3/2) * (2/1)
= √3

Therefore, the exact value of the function tan(π/3) is √3.