Given the function f (x) = sin (Wx + φ) (W > 0, - π / 2 ≤≤ π / 2), the distance between two adjacent highest and lowest points on the image is 2 √ 2 If f (x) passes through point (2, - 1 / 2), then f (x)=

Given the function f (x) = sin (Wx + φ) (W > 0, - π / 2 ≤≤ π / 2), the distance between two adjacent highest and lowest points on the image is 2 √ 2 If f (x) passes through point (2, - 1 / 2), then f (x)=

Because the coefficient in F (x) = sin (ω x + φ) is 1, the maximum and minimum values are - 1 and 1 respectively. The two-point ordinate difference is 2, so the abscissa difference is: √ [(2 √ 2) &# 178; - 2 & # 178;] = 2, so the half period is 2, the period T is 4, and ω = 2 π / T = π / 2 is substituted into the point (2, - 1 / 2)