If sin B=1/4, pi/2 < B < pi, find the exact value of sin 3B
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We know that sin 3x = 3 sin x - 4 (sin x)^3
Now sin B is given as 1/4.
sin 3B = 3 sin B - 4(sin B)^3
=> 3* (1/4) - 4(1/4)^3
=> 3/4 - 1/16
=> (12 - 1)/16
=> 11/16
Therefore sin 3B = 11/16
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We know that sin 3B = 3sin B - 4 (sin B)^3.
If B is in the second quadrant, we'll have to determine where it's located 3B angle, to determine if the value of sin 3B is positive or negative.
pi/2 < B < pi
We'll multiply by 3:
3pi/2 < 3B < 3pi
The angle is located in the first quadrant, where the sine function is positive.
sin 3B = 3sin B - 4 (sin B)^3
sin 3B = 3/4 - 4 (1/4)^3
sin 3B = 3/4 - 1/16
sin 3B = (12-1)/16
sin 3B = 11/16
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