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25 December, 00:04

Use a calculator to solve the equation on the interval [0, 2π). Round to the nearest hundredth of a radian. sin 2x - sin x = 0 : 0, 1.05, 3.14, 5.24 1.05, 3.14, 5.24 0, 2.09, 4.19 0, 2.09, 3.14, 4.19

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  1. 25 December, 02:56
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    Sin 2x - sin x=0

    Using the trigonometric identity: sin 2x=2 sinx cosx

    2 sinx cosx - sinx = 0

    Common factor sinx

    sinx (2 cosx - 1) = 0

    Two options:

    1) sinx=0

    on the interval [0,2π), the sinx=0 for x=0 and x = π=3.1416→x=3.14

    2) 2 cosx - 1=0

    Solving for cosx

    2 cosx-1+1=0+1

    2 cosx = 1

    Dividing by 2 both sides of the equation:

    (2 cosx) / 2=1/2

    cosx=1/2

    cosx is positive in first and fourth quadrant:

    First quadrant cosx=1/2→x=cos^ (-1) (1/2) →x = π/3=3.1416/3→x=1.05

    Fourth quadrant: x = 2π-π/3 = (6π-π) / 3→x=5 π/3=5 (3.1416) / 3→x=5.24

    Answer: Solutions: x=0, 1.05, 3.14, and 5.24
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