What is the value of x in radian if sinx = 3x/4? Thank you.?

2018-03-26 3:06 pm

回答 (4)

2018-03-26 7:50 pm
I solved it graphically for you
x = -1.276, 0 or 1.276
See graph
https://www.desmos.com/calculator/ewklp4xlp2
2018-03-26 3:37 pm
Solve by numerical or graphical methods to yield x ≈ ±1.275698 or 0
2018-03-26 8:13 pm
sin x = 3x/4
sin x - 3x/4 = 0

f(x)= sin x - 3x/4
f'(x) = cos x - 3/4

Apply Newton's method and solve
Let the guess value x0= 1
x0 = 1.000000000
x1 = x0 - f(x0) / f'(x0) = 1 - (0.09147098) / (-0.20969769) = 1.436204056
x2 = x1 - f(x1) / f'(x1) = 1.43620406 - (-0.08619692) / (-0.61581372) = 1.296231668
x3 = x2 - f(x2) / f'(x2) = 1.29623167 - (-0.00963043) / (-0.47887207) = 1.276121017
x4 = x3 - f(x3) / f'(x3) = 1.27612102 - (-0.00019427) / (-0.45957083) = 1.275698295
x5 = x4 - f(x4) / f'(x4) = 1.2756983 - (-9e-8) / (-0.45916635) = 1.275698109
x6 = x5 - f(x5) / f'(x5) = 1.27569811 - (0) / (-0.45916618) = 1.275698109

x= 1.275698109 radians
= 73.09°
2018-03-26 4:11 pm
I am going to take a guess that should perhaps be :-
x = 3π/4
sin 3π/4 = 1/√2


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