Решите тригонометрическое уравнение:
И пожалуйста, можете объяснить как решать.
a) sin2x = 0
x = 0+πn
x = πn\2
b) cos(x+π\4) = -1
x-π\4 = π+2πn
x = π+2πn+π\4
x = 5π\4+2πn
g) sin(9π\2+x) = -19π\2+x = -π\2+2πnx = -π\2+2πn-9π\2 x = -5π+2πn
v) sin(5π+x) = 1
5π+x = π\2+2πnx = π\2+2πn-5π x = -9π\2+2πn
d) 4cos(2x-π\4) = 0
cos(2x-π\4) = 0
2x-π\4 = π\2+πn
2x = π\2+πn+π\4
2х = 3π\4+πn
х = 3π\8+πn\2
e) 1\7sin(x+3π\2) = 1
sin(x+3π\2) = 7
sin≠7 так как -1<sinA<1, ⇒ нет решений
=)..€∫∫
Copyright © 2024 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
a) sin2x = 0
x = 0+πn
x = πn\2
b) cos(x+π\4) = -1
x-π\4 = π+2πn
x = π+2πn+π\4
x = 5π\4+2πn
g) sin(9π\2+x) = -1
9π\2+x = -π\2+2πn
x = -π\2+2πn-9π\2
x = -5π+2πn
v) sin(5π+x) = 1
5π+x = π\2+2πn
x = π\2+2πn-5π
x = -9π\2+2πn
d) 4cos(2x-π\4) = 0
cos(2x-π\4) = 0
2x-π\4 = π\2+πn
2x = π\2+πn+π\4
2х = 3π\4+πn
х = 3π\8+πn\2
e) 1\7sin(x+3π\2) = 1
sin(x+3π\2) = 7
sin≠7 так как -1<sinA<1, ⇒ нет решений
=)..€∫∫