2 I. Interpreting Sine Functions The sine function, y = sin θ, matches the measure θ of an angle in standard position with the y – coordinate on the unit circle.The periodic sine function has one cycle every 360° or 2πHence the sine of any degree greater than 2π, then the cycle is repeated.
3 The x-axis or domain will be thought of in terms of theta, θ When graphing you have to pay attention to the domain of theta. Trig Cycles are repeated once every 360 degrees or 2π
9 II. Properties of the Sine Function y = a sin bθІaІ = the amplitude (the highest and lowest points on the curves.)b = the number of cycles the curve makes from 0 to 2π2π / b = the period of the cycle
10 Steps to Graphing y = a sin bθ Step 1: draw your reference curveStep 2: identify the domain and set up your graph.Step 3: identify the amplitude and documentStep 4: identify the number of cycles in the domain that you have to graphStep 4: identify the period you need to create one cycleStep 5: Alter graph in needed in increments of 4 units on the theta axis to meet the criteria of the total cycles.
11 Example 2: how many cycles does the following have in the domain from 0 to 2π? Give the amplitude and period as well.A) y = -5 sin 2θB) f(x) = .5 sin .5θ
12 Example 3: Graph the following. (check on the calculator) A) y = -2 sin 2θ, for 0 < θ < 2πB) y = 5 sin θ, for 0 < θ < 2πC) y = ½ sin .5θ, for 0 < θ < 2π