Problem with sin in a question: "Find all real numbers x such that sin(x) =√3/2"

[krizzo]

Problem with sin in a question: "Find all real numbers x such that sin(x) =√3/2"

Hello everybody,
I'm doing my maths assignment and I came across a problem that I'm not sure of. My question asks find all real numbers x such that sin(x) =√3/2. So this is what I did:
sinx=√3/2
x=sin-1√3/2
x=60 degrees
Knowing that Sin is positive in first and second quadrant I say that x=60 degrees and x=180-60 which is 120 degrees.
My question is that if I have √3/2 does that only asks me for all positive real numbers or should I go further to 180+60 and 360-60 ??
Thank you

 

[stapel]

Find all real numbers x such that sin(x) = √3/2.

So this is what I did:

sin(x) = √3/2
x = sin^-1(√3/2}
x = 60 degrees

Knowing that sine is positive in the first and second quadrants, I say that x = 60 degrees and x = 180-60 degrees = 120 degrees.

Okay; those are the two real-valued solutions which fall within the first period. How find a formula for all real-valued solutions.

My question is that if I have √3/2 does that only asks me for all positive real numbers or should I go further to 180+60 and 360-60 ??

I'm sorry, but I don't know what you mean by "if I have √3/2 does that only asks me for all positive real numbers"...? Did you mean something like, "If the question asks me for only all positive real numbers x such that sin(x) = √3/2, does this mean that I should only find the real numbers that occur in the first period?"? What do you mean by "should I go further..." (since the sine does not evaluate to the specified number for x = 240 degrees, nor for x = 300 degrees)?

Please be complete. Thank you!