Solve for x in the following equation : 23 sin⁡(x+π/2)+90=76?

I am completely lost on this problem

6 Answers

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  • MyRank
    Lv 6
    3 weeks ago

    23sin(x+π/2) + 90 = 76

    23sin (π/2 + x) = 76 - 9023cosx = -14cosx = -14/23x = cos⁻¹(-14/23).

  • Como
    Lv 7
    3 weeks ago

    :-

    23 ( sin x cos π/2 + cos x sin π/2 ) = - 14

    cos x = -14/23

    x = (180 - 52•5) °, (180 + 52•5) °

    x = 127•5 ° , 232•5 °

  • 3 weeks ago

    Subtract 90 each side. What do you get?

    Then divide by 23 each side. What do u get?

    Answer these and we will proceed.

    Ok. Now ask yourself, what angle θ such that sin(θ) = -14/23?

    Using ur calculator, arcsin(-14/23) gives -37.5 and not 37.5.

    But note the π/2 in your sin(x+π/2) indicating that you are working in radians.

    So put ur calculator in rad.

    arcsin(-14/23) = ?

    Ok, yes its -0.654.

    that is, the angle θ such that sin(θ) = -14/23 is θ = -0.654.

    But YOUR angle is θ = x+π/2 = -0.654.

    Thus, x = -0.654 - π/2 = ?

    BUT careful. The eqs sin(θ) = -14/23 actually has two primary solutions [think of your trig circle]. They are θ = -0.654 and -2.487 rad. BUT, all multiple of 2π of these are thus solutions. IOW,

    θ = -0.654 + 2nπ & -2.487 + 2nπ, for any integer n.

    Thus, x + π/2 = -0.654 + 2nπ & -2.487 + 2nπ. Thus,

    x = -0.654 + 2nπ - π/2 & -2.487 + 2nπ - π/2.

    Lets try one for fun: 23sin( (-2.487 + 2*9*π - π/2) + π/2) + 98 = ?

    U might want to use more accuracy in your result of arcsin.

  • sin(x + pi/2) = sin(x)cos(pi/2) + cos(x)sin(pi/2) = cos(x)

    23 * sin(x + pi/2) + 90 = 76

    23 * cos(x) + 90 = 76

    23 * cos(x) = -14

    cos(x) = -14/23

    x = arccos(-14/23)

    x = arccos(-14/23) + 2pi * k, where k is an integer.

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  • oubaas
    Lv 7
    3 weeks ago

    23 sin⁡(x+π/2) = 76-90 = -14

    sin⁡(x+π/2) = -14/23

    arcsin (14/23) = 0.654 rad

    x = (π/2+0.654) rad

  • rotchm
    Lv 7
    3 weeks ago

    Subtract 90 each side. What do you get?

    Then divide by 23 each side. What do u get?

    Answer these and we will proceed. 

    Ok. Now ask yourself, what angle θ such that sin(θ) = -14/23?

    Using ur calculator, arcsin(-14/23) gives -37.5 and not 37.5. 

    But note the π/2 in your sin(x+π/2) indicating that you are working in radians.

    So put ur calculator in rad. 

    arcsin(-14/23) = ?

    Nope, its not 0.654 radians . Try again.

    Ok, yes its -0.654.

    that is, the angle θ such that sin(θ) = -14/23 is θ = -0.654.

    But YOUR angle is θ = x+π/2 = -0.654.

    Thus, x = -0.654 - π/2 = ?

    BUT careful. The eqs sin(θ) = -14/23 actually has two primary solutions [think of your trig circle]. They are θ = -0.654 and -2.487 rad. BUT, all multiple of 2π of these are thus solutions. IOW, 

    θ = -0.654 + 2nπ  &  -2.487 + 2nπ, for any integer n. 

    Thus, x + π/2 = -0.654 + 2nπ & -2.487 + 2nπ. Thus,

    x =  -0.654 + 2nπ - π/2 & -2.487 + 2nπ - π/2.

    Lets try one for fun:  23sin( (-2.487 + 2*5*π - π/2) + π/2) + 90 = ?

    U might want to use more accuracy in your result of arcsin. 

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