Question

Найдите наименьший положительный период функции а) f(x)=sin(π / 2+π / 6) б) f(x)=ctg 3x

Answer 1

Решение
a)  f(x)=sin(π / 2+π / 6) = cos(π / 6) = √3/2
б) f(x )= ctg 3x
T = π/3

Answer 2

I can help you with your math question.

To find the smallest positive period of a function, you need to find the smallest positive number T such that f(x + T) = f(x) for all x in the domain of f.

a) f(x) = sin(π / 2 + π / 6)

This function is a sinusoid with a phase shift of π / 2 + π / 6. The period of a sinusoid is 2π / k, where k is the coefficient of x. In this case, k = 1, so the period is 2π / 1 = 2π. This is the smallest positive period of f(x).

b) f(x) = ctg(3x)

This function is a cotangent with a coefficient of 3. The period of a cotangent is π / k, where k is the coefficient of x. In this case, k = 3, so the period is π / 3. This is the smallest positive period of f(x).

You can find more information about periodic functions and their properties on these websites, , , , and . I hope this helps.