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If sin B=1/4, pi/2 < B < pi, find the exact value of sin 3B

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justaguide eNotes educator | Certified Educator

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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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giorgiana1976 | Student

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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