§ 30: 30.33 (1)

30.33 Побудуйте графік функції:

1) y = sin(arcsin x); D(y) = [–1; 1]; y = sin(arcsin x) = x.

2) y = cos(arcsinx); D(y) = [–1; 1]; y = cos(arcsinx) = [№ 30.22] =

= 1- x2 ⇔ y² = 1 – x²; x² + y² = 1;

y ≥ 0; y ≥ 0;

x ∈ [–1; 1]; x ∈ [–1; 1];

3) y = cos(2arcsinx); D(y) = [–1; 1]; y = cos(2arcsinx) = 1 – 2sin² (arcsinx) = 1 – 2x².

4) y = sin(arcsin x + arccos x); D(y); [–1; 1]; y = sin(arcsin x) • cos(arccos x) + cos(arcsin x) • sin(arccos x) = x • x + 1- x2 • 1- x2 = x² + 1 – x² = 1.