determine the period of the function.
y = cot 4t
To determine the period of the function y = cot 4t, we need to understand the properties of the cotangent function.
The cotangent function can be expressed as cot x = 1/tan x, where tan x represents the tangent function. The period of the cotangent function is the same as the period of the tangent function.
The general form of the tangent function is tan x = a * tan(bx−c) + d, where a, b, c, and d are constants.
In this case, we have y = cot 4t, which is equivalent to y = 1/tan 4t.
Comparing this with the general form of the tangent function, we can see that a = 1, b = 4, c = 0, and d = 0.
To find the period of the tangent function, we use the formula:
Period = (2π) / |b|
Substituting the value of b = 4 into the formula, we get:
Period = (2π) / |4|
Period = (2π) / 4
Simplifying, we find:
Period = π / 2
Therefore, the period of the function y = cot 4t is π / 2.
To determine the period of the function y = cot 4t, we need to understand the characteristics of the cotangent function.
The cotangent function is periodic with a period of π, which means that it repeats its values every π units. However, in this case, the function is multiplied by 4t, which affects the period.
To find the adjusted period, we divide the original period (π) by the coefficient in front of t, which is 4. Therefore, the adjusted period for y = cot 4t is:
π / 4
Hence, the period of the function y = cot 4t is π / 4 units.