Question

sin(theat/2)=1/2
How would you solve this???

Answer 1

you have to know your special values for trig functions
what is arcsin(1/2) ?

Answer 2

That would be 60.

Because the question is asking sin of what divided by a half equals 30.

Since sin30 = 1/2;
30 x 2 = 60;

And therefore theta is 60 because sin (60/2) is equal to 1/2.

Answer 3

first use the inverse trig function arcsin:\[\sin(\frac\theta2)=\frac12\implies\frac\theta2=\sin^{-1}(\frac12)\]so at what angle x is sinx=1/2 ?

Answer 4

pi/6=x

what is a general formula?

Answer 5

to find x in the above question?
there isn't one, you just got lucky that 1/2 is a special value of sinx
so is sinx=sqrt3/2 and such
if it were sinx=0.27368... or something funky like that, you would have ot break out the calculator and use the arcsin function