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/2. (Hint: The function on the right is tan π/3.)
To find the value of tan(π/3), we first need to locate the angle π/3 on the unit circle.
Since s = π/2, we know that we have already passed the y-axis and are currently at the point (0,1) on the unit circle.
Next, we need to find the point on the unit circle that corresponds to the angle π/3. Since this angle is in the first quadrant, we know that both the x-coordinate and y-coordinate of this point will be positive.
To find the x-coordinate, we can use the cosine function. The cosine of π/3 is equal to 1/2, so the x-coordinate of the point is 1/2.
To find the y-coordinate, we can use the sine function. The sine of π/3 is equal to √3/2, so the y-coordinate of the point is √3/2.
Therefore, the point on the unit circle that corresponds to the angle π/3 is (1/2, √3/2).
Now, we can find the value of tan(π/3) by taking the ratio of the y-coordinate to the x-coordinate of the point on the unit circle.
tan(π/3) = (√3/2) / (1/2)
To simplify, we can multiply the numerator and denominator by 2:
tan(π/3) = (√3/2) * (2/1)
tan(π/3) = √3
So, the exact value of tan(π/3) is √3.