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

The simple interest on Rs. 4000 at 5% per annum for 2 years is:

View Question

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

View Question

If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

View Question

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

View Question

What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

View Question

What is the square root of 144?

View Question

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

View Question

A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

View Question

The base of a triangle is 10 cm and its height is 6 cm. What is its area?

View Question

If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

View Question