Find the complete solution if sin(x) = -.9854

[Vol]

Hi. I can't understand what this problem is asking. Here it is:
"Find the complete solution (to the nearest tenth) if sin(theta) = -98544973 and 0 </= theta < 2pi."
The answer is 4.5 and 4.9 it says.
I know that arcsin(-98544973) = -80.214 degrees = 279.8 degs.
I know that -98544973 is the length of the opposite leg to the reference angle in the unit circle for sine below the x-axis.
So, where does 4.5 and 4.9 come from? Stumped

 

[Deleted member 4993]

Hi. I can't understand what this problem is asking. Here it is:
"Find the complete solution (to the nearest tenth) if sin(theta) = -98544973 and 0 </= theta < 2pi."
The answer is 4.5 and 4.9 it says.
I know that arcsin(-98544973) = -80.214 degrees = 279.8 degs.
I know that -98544973 is the length of the opposite leg to the reference angle in the unit circle for sine below the x-axis.
So, where does 4.5 and 4.9 come from? Stumped

There is a typo in this problem statement and your work.

-1 ≤ sin(Θ) ≤ 1 ............for any and all values of Θ ............. so -98544973 is probably -0.98544973 (it is stated correctly in the subject-line)

Since the domain is defined in radians, instead of calculating in degrees - calculate in radians.

Your solutions should be in the third quadrant and and the fourth quadrant (very near to 3π/2)

 

[Vol]

Oh, right. It's a typo. Sorry.
But arcsin -.98544973 = -1.4 radians. I still don't get where the 4.5 and the 4.9 comes from. What am I not getting? It must be something simple I am just not seeing.

 

[Deleted member 4993]

Oh, right. It's a typo. Sorry.
But arcsin -.98544973 = -1.4 radians. I still don't get where the 4.5 and the 4.9 comes from. What am I not getting? It must be something simple I am just not seeing.

Θ = -1.4 radians

That's a negative value - but your required domain is positive!!(0 ≤ Θ < 2π). .........so...........

 

[pka]

But arcsin -.98544973 = -1.4 radians. I still don't get where the 4.5 and the 4.9 comes from. What am I not getting? It must be something simple I am just not seeing.

I do not see how \(-1,4\) or either \(4.5,~4.9\) are at all related to this question. See here for a definitive solution.

 

[Dr.Peterson]

I do not see how \(-1,4\) or either \(4.5,~4.9\) are at all related to this question. See here for a definitive solution.

You do see -1.4 (radians) as part of the work. That's the inverse sine you provided as the solution.

What amazes me is that they give so many decimal places of the sine, but then round the answer to one decimal place.

The solutions in the given range are, of course, \(2\pi-1.4 = 4.883185\approx 4.9\) and \(\pi+1.4 = 4.54159\approx 4.5\).

 

[Deleted member 4993]

Θ = -1.4 radians

That's a negative value - but your required domain is positive!!(0 ≤ Θ < 2π). .........so...........

Use:

sin(Θ) = sin(π - Θ) ........................... and

sin(Θ) = sin(2*π + Θ)

Don't forget that all these calculations are in radian.

 

[Vol]

Oh, I get it now. A scientific calculator will automatically match domain and range. I was in the wrong part of the phase graph. And there are always two inputs for one output within a period except at the maxima and minima.