Inverse Trig Functions?

Question

Find the exact value of the inverse trig function.

sin(cos^-1 (1/2))

Answer 1

sin(cos^-1 (1/2))
=?

let x=cos^-1 (1/2)
1/2=cosx
x=60

sin60=sqrt(3)/2

Answer 2

NO! the arc's or specifically sin^-1, cos^-1, tan^-1 are functions used to find angles. This is why they are sometimes called arcsin, arccos, arctan, to avoid confusion with 'inverses'. In the case of trig fucntions, cosec, sec, and cot can be seen as reciprocals rather than inverses. Inputting the reciprocals into a calculator is simple. Eg. for sec(x) simply put in cos(x), but put a 1 over it. should look like this: Y=1/(cos(x)) graphing gives the graph of Y=sec(x) Get it?

Answer 3

cos x = 1/2

since cos = adj / hyp

we know that
adj = 1
hyp = 2

using pythagorean theorem, we find
opp = sqrt 3

sin x = opp / hyp = (sqrt 3) / 2

Answer 4

cos^-1(1/2) = 60

sin(60) = sqrt(3)/2

so the answer is sqrt(3)/2

Answer 5

♠ y=sin(acos(1/2)); 1/2=cos60°; y=sin60 =0.5*sqrt(3);