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.
If a+b = 10 and ab = 21, what is the value of a^3 + b^3?
View QuestionIf x = 2 and y = 3, what is the value of (x^2 + y^2)?
View QuestionThe sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?
View QuestionIf a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?
View QuestionHow many diagonals does a pentagon have?
View QuestionA triangle has angles 60°, 60°, and 60°. What type of triangle is it?
View QuestionA sum of money doubles itself in 5 years at simple interest. What is the rate of interest?
View QuestionIf x^2 - 5x + 6 = 0, what are the roots?
View QuestionWhat is the greatest common divisor (GCD) of 36 and 48?
View QuestionA car travels 240 km in 4 hours. What is its average speed?
View Question