Question

sin(2arcsin(-1/3)) please explain how to get this without the use of a calculator

Answer 1

table of sines id suppose

Answer 2

or draw a picture

Answer 3

since sin is defined as over/hyp; we have a triangle that is 1 over and 3 hyp but somewhere on the underside of a circle

Answer 4

doubling that "angle" will give us the values of x and y for the outter sin

Answer 5

since the angle is going to have the same absolute value; it might be simpler to draw it in a normal position tho

Answer 6

sin(2t) = 2sin(t)cos(t) right?

Answer 7

sin(t) = -1/3

cos(t) = sqrt(1-sin^2(t))
= sqrt(1 - 1/9)
= sqrt(8/9)
= 2sqrt(2)/3

2*-1/3*2sqrt(2)/3 = -4sqrt(2)/9 i believe