Solve for x: 0⁰ < x< 360⁰ 1 + 5 \sin(x - 10 {0}^{0} ) = 0

Question

Solve for x: 0⁰ < x< 360⁰
1 + 5 \sin(x - 10 {0}^{0} )  = 0

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Yến Oanh 1 week 2021-07-21T22:55:23+00:00 1 Answers 1 views 0

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    2021-07-21T22:56:37+00:00

    Answer:

    x = 88.463°

    Step-by-step explanation:

    We are given a trigonometric equation and we need to find out the value of x. The angle x lies between 0° and 360° . That is ,

    \rm\implies\red{ 0^0 < x < 360^0 }

    Given trigonometric equation :

    \rm\implies\red{ 1 + 5 sin (x-100^0)=0 }

    Subtracting 1 both sides , we have ,

    \rm\implies 5sin( x - 100^0)= -1

    Divide both sides by 5 ,

    \rm\implies sin( x - 100^0)= \dfrac{-1}{5}

    This equation can be written as ,

    \rm\implies x - 100^0 =sin^{-1}\bigg(\dfrac{ -1}{5}\bigg) \\\\\rm\implies x - 100^0 = -11.53^0 \\\\\rm\implies x = 100^0-11.53^0\\\\\rm\implies\boxed{\bf x = 88.463^0}

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