Question

General Sine CurvesForf(x) = A sin ((2π/B)(x – C) +Didentify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.y = ½ sin (πx – x) + ½

Accepted Answer

Step 1: Start by comparing the given sine function y = ½ sin(πx - x) + ½ to the general sine function f(x) = A sin((2π/B)(x - C)) + D. Notice that the given function has a simplified argument inside the sine function, so simplify πx - x to (π - 1)x. Step 2: Identify the amplitude A. The amplitude is the coefficient of the sine function, which in this case is ½. Therefore, A = ½. Step 3: Identify the period B. The period is determined by the coefficient of x inside the sine function. Here, the coefficient of x is (π - 1). The period B is calculated as B = 2π / |π - 1|. Step 4: Identify the phase shift C. The phase shift is determined by the term (x - C) inside the sine function. Since there is no explicit constant added or subtracted from x in the argument, C = 0 (no horizontal shift). Step 5: Identify the vertical shift D. The vertical shift is the constant added outside the sine function, which in this case is ½. Therefore, D = ½. With these values (A = ½, B = 2π / |π - 1|, C = 0, D = ½), you can now sketch the graph of the sine function.

General Sine Curves

For

f(x) = A sin ((2π/B)(x – C) +D

identify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.

y = ½ sin (πx – x) + ½

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Amplitude

Period

Phase Shift and Vertical Shift