2006-11-09 13:28:21 · 5 answers · asked by bunches999 4 in Science & Mathematics ➔ Mathematics
Given
sin 3x = 1/2
Get arcsin of both sides
arcsin (sin 3x) = arcsin (1/2)
The left side simplifies as 3x. The right side varies.
Let k be any integer. Thus,
3x = π/4 + 2kπ and
3x = 3π/4 + 2kπ
Thus,
3x = (π + 8kπ)/4 and
3x = (3π + 8kπ)/4
Therefore,
x = π/12 (8k + 1) and
x = π/12 (8k + 3)
where k is ANY integer. Enumerating, we have,
x = ... -5π/4, -7π/12, π/12, 3π/4, 17π/12, 25π/12, 11π/4, ...
x = ... -13π/12, -5π/12, π/4, 11π/12, 19π/12, 9π/4, 35π/12, ...
^_^
2006-11-09 23:30:55 · answer #1 · answered by kevin! 5 · 0⤊ 0⤋
arcsin (sin(3x)) = 3x
arcsin (1/2) = 30°
3x = 30°
x = 10°
2006-11-09 13:33:45 · answer #2 · answered by AnswerMan 4 · 0⤊ 0⤋
sin(3x) = (1/2)
3x = sin^-1(1/2)
3x = 30° or 150°
x = 10° or 50°
ANS : 10° or 50°
2006-11-09 14:33:47 · answer #3 · answered by Sherman81 6 · 0⤊ 0⤋
Take the inverse sin of both sides. You get:
3x = pi/6
x = pi/18
2006-11-09 13:33:22 · answer #4 · answered by Anonymous · 0⤊ 0⤋
borat!
2006-11-09 13:36:43 · answer #5 · answered by ilina 2 · 0⤊ 0⤋