How do you find the \arcsin(\sin(\frac{7\pi}{6})) ?

meteraiqn 2022-01-22 Answered
How do you find the arcsin(sin(7π6)) ?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

gekraamdbk
Answered 2022-01-23 Author has 13 answers
The answer is:
arcsin(sin(7π6))=π6
The range of a function arcsin(x) is, by definition.
π2arcsin(x)π2
It means that we have to find an angle α that lies between π2 and π2 and whose sin(α) equals to a sin(7π6).
From trigonometry we know that
sin(ϕ+π)=sin(ϕ)
for any angle ϕ.
This is easy to see if use the definition of a sine as an ordinate of the end of a radius in the unit circle that forms an angle ϕ with the X-axis (counterclockwise from the X-axis to a radius).
We also know that since is an odd function, that is sin(ϕ)=sin(ϕ)
We will use both properties as follows:
sin(7π6)=sin(π6+π)=sin(π6)=sin(π6)
As we see, the angle α=π6 first our conditions. It is in the range from π2 to π2 and its sine equals to sin(7π6). Therefore, it's a correct answer to a problem.
Not exactly what you’re looking for?
Ask My Question
enguinhispi
Answered 2022-01-24 Author has 15 answers
So:
arcsin=sin1
sin1(sin(7π6))
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the third quadrant.
sin1(sin(π6))
The exact value of sin(π6) is 12.
sin1(12)
The exact value of sin1(12) is π6
The result can be shown in multiple forms.
Exact Form:
π6
Decimal Form:
0.52359877
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more