Find the Equation of a Trigonometric Function Given Its Graph - Grade 12

In this video, it is shown, through an example, how to find the equation of a trigonometric function, given by its graph. The function suggested is of the form: V(t) = A cos (Bt + C) + D where t is the variable. Formulas to find the parameters A (chosen to be positive) and D describing the amplitude and vertical shift of the trigonometric function are deduced: A = (Vmax - Vmin) / 2 , gives A greater than zero. D = A = (Vmax +Vmin) / 2 The period of the function is determined from its graph and the formula: Period = 2 pi / B , B greater than zero. is used to find B. The parameter C is related to the phase shift and is determined by locating a maximum (or a minimum) of the function using the graph. Assume the maximum is at t = T, and write the equation V(T) = A cos (B T + C) + D = A + D and knowing A, B, D, and T, solve a trigonometric equation for C which gives an infinite number of solutions. More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html