Thread: coordinates and trigonometry

I have to find the coordinates for S(i).

My attempt :

OP = 1 * 1/2 = 1/2

(1/2)² + x² = 1²

x = √(3)/2

cos^-1(√(3)/2) = 30

sin^-1(1/2) = 30

t = 30

cos(2*t) = cos(60) = 1/2

sin(2*t) = sin(60) =√(3)/2

S(i) = (1,2 , √(3)/2 )

t is not 30°. t is arctan(1/2). And so your coordinates (cos(2t),sin(2t)) = ?

Can you try to explain why t= arctan(1/2) because I can't see it.
And can't I use arccos and arcsin instead of arctan?

The angle of inclination of a line having slope is .

.

Now, use the double-angle identities for sine and cosine and:

Thank you.