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

I am completely lost on this problem

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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.

• 3 weeks ago

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.

• oubaas
Lv 7
3 weeks ago

23 sin⁡(x+π/2) = 76-90 = -14

sin⁡(x+π/2) = -14/23

• 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.