Topic Details (Notes format)

How to Identify Amplitude, Period, Phase Shift, and Vertical Shift in Trig Functions

Subject: Mathematics

Book: Maths Mastery

For y=A sin(Bx–C)+D or y=A cos(Bx–C)+D:
• Amplitude = |A|, the peak displacement.
• Period = 2π/B for sine/cosine (π/B for tangent).
• Phase Shift = C/B, horizontally shifting the graph.
• Vertical Shift = D, moving it up or down.
Example: y=3 sin(2x–π)+1 has amplitude 3, period π, phase shift π/2, vertical shift 1. Understanding these parameters is pivotal in wave analysis (light, sound, tides), engineering vibrations, or cyclical data modeling. Mastery brings clarity to transformations and deeper intuition for describing recurring phenomena mathematically.

Practice Questions

If x + 1/x = 5, what is the value of x^2 + 1/x^2?

View Question

The probability of getting an even number when rolling a die is:

View Question

What is the value of log₃(27)?

View Question

If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

View Question

The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

View Question

The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

View Question

If the sum of three consecutive integers is 72, what are the integers?

View Question

What is the sum of the interior angles of a hexagon?

View Question

What is the remainder when 5^100 is divided by 3?

View Question

If x = 3 and y = 4, what is the value of x^2 + y^2?

View Question