Question

Find the period of the function y = 3∕2 tan(1∕3x). question 10 options:

a) π∕3
b) 3π
c) π∕6
d) π

Answer 1

The period of the function y = 3/2 tan(1/3x) is found by dividing the normal period of tan(x), which is π, by the absolute value of the coefficient inside the function, yielding a period of 3π

Step-by-step explanation:

The question asks us to find the period of the trigonometric function
`y = \((3)/(2)\) tan(\((1)/(3)x\)).`

The period of the tangent function, tan(x), is π.

However, in this case, the function has been altered by a coefficient of
`\((1)/(3)\)` inside the tangent function, which affects the period.

To find the period of
`y = \((3)/(2)\) tan(\((1)/(3)x\))`, we divide the normal period of the tangent function by the absolute value of the coefficient inside the function.

The new period is found by:
Period = π/(|1/3|) = 3π.

Therefore, the correct option for the period is option b) 3π.