For the function y=3sin(2x-π/6), find the amplitude, period, phase shift, maximum and minimum values.

Amplitude 3, period pi, phase shift pi/12 to the right, maximum 3, minimum -3

For the function $y = 3 s in (2 x - \frac{π}{6})$ , find the amplitude, period, phase shift, maximum and minimum values.

medium 3 marks Class 11 · Mathematics · Trigonometric Functions

Answer

Amplitude

3

, period

p i

, phase shift

\frac{p i}{12}

to the right, maximum

3

, minimum

- 3

The correct answer is Amplitude $3$ , period $p i$ , phase shift $\frac{p i}{12}$ to the right, maximum $3$ , minimum $- 3$ — Minimum occurs when $s in (argument) = - 1$ , giving $y_{min} = 3 (- 1) = - 3$ at $x = \frac{π}{12} + π + 2 k p i$ .

Step-by-step solution

Compare $y = 3 s in (2 x - \frac{p i}{6})$ with the standard form $y = a s in (b x - c)$ .
Amplitude $a = ∣3∣ = 3$ .
Period $T = \frac{2 p i}{∣ b ∣} = \frac{2 p i}{2} = p i$ .
Rewrite $2 x - \frac{π}{6} = 2 (x - \frac{π}{12})$ ; thus the phase shift is $\frac{π}{12}$ to the right.
Maximum occurs when $s in (argument) = 1$ , giving $y_{ma x} = 3 (1) = 3$ at $x = \frac{π}{12} + 2 k p i$ .
Minimum occurs when $s in (argument) = - 1$ , giving $y_{min} = 3 (- 1) = - 3$ at $x = \frac{π}{12} + π + 2 k p i$ .

Common mistake: Using the wrong formula for the period or sign error in the phase shift

Concept tested: Amplitude‑phase form of trig functions

Published 1 October 2026 · How this solution was prepared and checked

← All Trigonometric Functions questions

For the function y=3sin(2x−6π​), find the amplitude, period, phase shift, maximum and minimum values.

Step-by-step solution

For the function $y = 3 s in (2 x - \frac{π}{6})$ , find the amplitude, period, phase shift, maximum and minimum values.