# Tutorial on Sine Functions (1)- Problems

 This is a tutorial on sine function problems. Examples with detailed solutions and explanations are included. Example - Problem 1: Find a, b and c included in the definition the sine function f given by f(x) = a*sin(bx + c) such that the maximum value of f(x) is 6, f(0) = 6 and the period of the graph of function f is equal to pi. a, b and c are positive and c is less than 2pi. Solution to Problem 1: The maximum value 6 gives the amplitude | a | = 6 Solve the above equation for a and select the positive value. a = 6 The period may be used to find b using period = 2*pi / | b | = pi Solve for | b | | b | = 2 Solve for b and select the positive value b = 2 Substitute 6 for a in the formula of the function and use f(0) = 6 to write an equation in c. 6 = 6*sin(b*0 + c) Which gives sin(c) = 1 Solve for c c = pi/2 + k(2*pi) , where k is an integer. There is an infinite number of solutions for c. Select k = 0 since it is the only value that gives c > 0 and less that 2*pi, which gives c = pi / 2 Function f is given by f(x) = 6*sin(2x + pi/2) For checking, part of the graph of f is shown below. Check the period and f(0) = 6 and that the maximum value of f(x) is 6. Matched Problem 1: Find a, b and c in the sine function f given by f(x) = a*sin(bx + c) such that the minimum value of f is -3, f(0) = -3 and the period of the graph of the function is equal to 4*pi. a, b and c are positive and c is less than 2 pi. More references on Trigonometry Problems. Match Sine Functions to Graphs. Excellent activity where graphs and functions are matched.