Trig question?

Question

Which set of expressions, where N is an integer, give all possible values of "sin^-1(√2/2)"

 

π is pi

 

a) (2π)N, π+(2π)N

b) π/4+(2π)n, 3π/4+(2π)N

c) π/6+ (2π)N, 5π/6+(2π)N

d)π+(2π)N, 2π+(2π)N

Answer 1

You are told that sin(x)=sqrt(2)/2.  This implies that x=45 degrees, which is pi/4 radians is one solution.

 

From the unit circle, you can see that another solution is x=pi-pi/4=3pi/4.

 

Finally, adding n2pi to either solution gives another solution, since that just takes you around the circle n times, leaving you at the same angle.

 

Choice (b) is correct.