4 sinx cosx=1
find x between 0 degrees to 360 degrees
2007-08-24 23:16:04 · 9 answers · asked by Stormy Knight 1 in Science & Mathematics ➔ Mathematics
sin(2x) = 2sin(x)cos(x) .... trig identity
4 sinx cosx = 2sin(2x) = 1
sin(2x) = 1/2 so 2x = 30 degrees or pi/6 radians
The sin is also positive in the second qudarant so:
2x = 150 degrees or 5pi/6
therefore x = 15 degrees or pi/12 radians
and x = 75 degrees or 5pi/12 radians
Check:
4sin(15)cos(15) = 4(.2588)(.9659) = 1
4sin(75)cos(75) = 4(.9659)(.2588) = 1
2007-08-24 23:27:40 · answer #1 · answered by Captain Mephisto 7 · 0⤊ 1⤋
4 sinx cosx=1
2(2sinx cos x) =1 From trigonometric identities
sin2x= 2 sin x cos x
2(sin2x)=1
sin2x=1/2
2x=Sin^-1 (1/2)
2x= 30
x=15 degrees, 180-15= 165 degrees
x=15 degrees
2007-08-24 23:31:43 · answer #2 · answered by ptolemy862000 4 · 0⤊ 1⤋
2sinxcosx = 2x1/4 = ½
sin(2x) = 1/2
2x = sininv(0.5)
2x = 30 degrees
x = 15 degrees in the first quadrant.
2x = 150 in the second quadrant ( sin is +ve in Ist and IInd quads).
x = 150/2 = 75 degrees.
2007-08-25 00:15:31 · answer #3 · answered by Anonymous · 0⤊ 0⤋
4 sinxcosx =1
Sinx cosx =1/4
Since the two are multiplied, separate them:
Sin x= 1/4 cos x = 1/4
x=InvSin (1/4) x = InvCos (1/4)
Not exact numbers; need a calculator. There will be two answers for Sin x and two answers for Cos x.
2007-08-24 23:38:48 · answer #4 · answered by james w 5 · 0⤊ 1⤋
2sinxcosx = 2x1/4 = ½
sin(2x) = 1/2
2x = sininv(0.5)
2x = 30 degrees
x = 15 degrees in the first quadrant.
2x = 150 in the second quadrant ( sin is +ve in Ist and IInd quads).
x = 150/2 = 75 degrees.
2007-08-24 23:52:22 · answer #5 · answered by Anonymous · 0⤊ 1⤋
2 ( 2 sin x cos x) = 1
( 2 sin x cos x) = 1/2
sin 2x = 1/2
2x = 30 deg
x = 15 deg
2x = 150
x = 75 deg
2007-08-24 23:30:38 · answer #6 · answered by CPUcate 6 · 0⤊ 1⤋
2sinxcosx=sin2x
=>4sinxcosx=2sin2x
by the problem,
2sin2x=1
or, sin2x=1/2=sin30 or sin(180-30)
x=15, or 75
2007-08-24 23:44:45 · answer #7 · answered by diya 1 · 0⤊ 1⤋
4sinxcosx = 1
=> 2sinxcosx = 1/2
=> sin2x = sin 30 deg
=> 2x = n180 deg (+ or --) 30 deg, n=0,1,2,
=> 2x = 30deg, 150deg, 390deg, 510deg.
=> x = 15deg, 75deg, 195deg, 255deg.
2007-08-24 23:43:03 · answer #8 · answered by sv 7 · 0⤊ 1⤋
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2016-10-09 05:14:52 · answer #9 · answered by ? 3 · 0⤊ 0⤋