GMAT GRE 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade 7th grade math 8th grade math 9th grade math 10th grade math 11th grade math 12th grade math Precalculus Worksheets Chapter wise Test MCQ's Math Dictionary Graph Dictionary Multiplicative tables Math Teasers NTSE Chinese Numbers CBSE Sample Papers 
Cosine GraphCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! Cosine Graph : Trigonometric function `cos x` is a periodic functions.Cosine function has maximum value as +1 and minimum as 1. Since cos(x) = cos x is an even function. The value of the functions `cos x` repeats in every 2π units of `x` . Therefore this function is periodic with a period of 2π Some definitions used in cosine curve are Amplitude: This is half the distance between the maximum and minimum values. The term `a` in the general form of the sinusoidal function represents the amplitude of this function. The amplitude is a constant for sinusoidal functions. Period: This is the smallest time needed for a function to execute one complete cycle. From the general form of cosine function, the period T can be written as T = 2π/ b Now let us come back to the simplest cosine function . y =a cos bx where a = amplitude . Period = 2π / b Cos (0) = 1 so cosine graph always start from 1. As b gets larger, the period decreases. Phase shift of cosine function y = a cos (bx + c ) + d Both b and c affect the phase shift or movement of graph
Phase shift =  c / b Period = 2π / b The phase shift is the amount that the curve is moved in a horizontal direction from its normal position. Phase shift, Negative > Left Displacement Phase shift, Positive > Right Displacement To find the phase shift , just make bx + c = 0 and solve. Example : y = 2 cos (2x +1 ) Here amplitude = a = 2 2x + 1 = 0 ⇒ x = 1/2 so Phase shift = 1/2. Period = 2π / b Period = 2π / b = 2π / 2 = π cosine graph Graph Dictionary Home Page Covid19 has affected physical interactions between people. Don't let it affect your learning.
More To Explore

