Find the values of the trigonometric functions tan 19π/3

Sure, let's solve this step by step.

Step 1: Simplify the angle The angle given is 19π/3. We know that the period of the tangent function is π, so we can subtract multiples of π from the angle until we get an angle that lies within the interval from -π/2 to π/2.

19π/3 = 6π + π/3

6π is a multiple of π, so the tangent of 19π/3 is the same as the tangent of π/3.

Step 2: Find the value of the tangent function The tangent of π/3 is √3.

So, tan(19π/3) = √3.