# coordinates and trigonometry

• October 27th 2012, 10:49 AM
Tala
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 )
• October 27th 2012, 11:06 AM
MarkFL
Re: coordinates and trigonometry
t is not 30°. t is arctan(1/2). And so your coordinates (cos(2t),sin(2t)) = ?
• October 27th 2012, 11:13 AM
Tala
Re: coordinates and trigonometry
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?
• October 27th 2012, 11:21 AM
MarkFL
Re: coordinates and trigonometry
The angle of inclination of a line having slope $m$ is $\tan^{-1}(m)$.

$m=\frac{\Delta y}{\Delta x}=\tan(\theta)\,\therefore\,\theta=\tan^{-1}(m)$.

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

$\sin(\tan^{-1}(x))=\frac{x}{\sqrt{x^2+1}}$

$\cos(\tan^{-1}(x))=\frac{1}{\sqrt{x^2+1}}$
• October 27th 2012, 11:38 AM
Tala
Re: coordinates and trigonometry
Thank you.