y = cot x have zero for value of x = nπ + π/2
What are trigonometric ratio ?
In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.
Given equation,
y = cot x
It is given that cot x = 0
hence,
cot is zero in the first and the third quadrants.
cot π/2 = 0.
In the first quadrant, x = π/2
In the third quadrant, x = π + π/2 as cot 3π/2 = 0
Thus, the principle solutions are: x = π/2, and 3π/2.
Now,
cot x = cot π/2
Therefore, x = nπ + π/2, where n ∈ Z is the general solution.
Hence, for value of x = nπ + π/2, graph of y = cot x have a zero.