Asked by Shre
Solve 4sin(pi/4x) = 3 for the four smallest positive solutions
Answers
Answered by
oobleck
4 sin(pi/4 x) = 3
sin(pi/4 x) = 3/4
pi/4 x = 0.848 + k*2π
x = 1.08 + k/2
so, x = 1.08, 1.58, 2.08, 2.58
sin(pi/4 x) = 3/4
pi/4 x = 0.848 + k*2π
x = 1.08 + k/2
so, x = 1.08, 1.58, 2.08, 2.58
Answered by
Reiny
sin(pi/4 x) = 3/4
so π/4x = .848 or π-.848
π/4x = .848 or πx/4 = 2.2935
x = 1.08 or x = 2.902
but the period of sin (πx/4) is 8, so
x = 1.08 + 8k or x = 2.902 + 8k , where k is an integer
4 smallest positive solutions:
x = 1.08, 2.902, 9.08, and 10.902
Verification:
https://www.wolframalpha.com/input/?i=y+%3D+3%2C+y+%3D+4sin%28%CF%80x%2F4%29+from+0+to+15+
so π/4x = .848 or π-.848
π/4x = .848 or πx/4 = 2.2935
x = 1.08 or x = 2.902
but the period of sin (πx/4) is 8, so
x = 1.08 + 8k or x = 2.902 + 8k , where k is an integer
4 smallest positive solutions:
x = 1.08, 2.902, 9.08, and 10.902
Verification:
https://www.wolframalpha.com/input/?i=y+%3D+3%2C+y+%3D+4sin%28%CF%80x%2F4%29+from+0+to+15+
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