Question

Find the Value of interval [0,2pie] such as that tan s= -radical3/3

Answer 1

The values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.

What is trigonometry and how is it assessed?
Simply put, trigonometric functions—also referred to as circular functions: are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The quadrants determine the values of the trigonometric functions.


Given, tan s = -(√3)/3 ⇒ tan s = -(√3)/(√3)² ⇒ tan s = (-1)/(√3)
Therefore, the simplified value of tangent of s is tan s = (-1)/(√3)
Again the interval of the function is [0, 2π), so only the second and fourth quadrants can contain the given value of tangent being negative.
For the value of s in second quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (π - (π/6)) ⇒ tan s = tan (5π/6) ⇒ s = 5π/6
For the value of s in the fourth quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (2π - (π/6)) ⇒ tan s = tan (11π/6) ⇒ s = 11π/6
Thus, the values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.

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