At what points does the helix
r(t) = sin t, cos t, t intersect the sphere
x^2 + y^2 + z^2 = 82?
(Round your answers to three decimal places. If an answer does not exist, enter DNE.)
(x, y, z) = __________________(smaller t-value)
(x, y, z) = ____________________larger t-value

Question

At what points does the helix 
r(t) = sin t, cos t, t intersect the sphere 
x^2 + y^2 + z^2 = 82?
 (Round your answers to three decimal places. If an answer does not exist, enter DNE.)
(x, y, z)	 = 	__________________(smaller t-value)
(x, y, z)	 = 	____________________larger t-value

anonymous · Answer

Hmmm, maybe solve for $t$ when $$
(\sin(t))^2 + (\cos(t))^2+(t)^2 = 82
$$

ganeshie8 · Answer

where were u stuck at ?

ganeshie8 · Answer

$(\sin(t))^2 + (\cos(t))^2+(t)^2 = 82$

$\sin^2(t) + \cos^2(t)+t^2 = 82$

ganeshie8 · Answer

u need to use a trig identity :
$\sin^2 \theta + \cos^2\theta = 1$

ganeshie8 · Answer

$\sin^2(t) + \cos^2(t)+t^2 = 82$

$1+t^2 = 82 $

solve $t $

anonymous · Answer

for smaller t-value ( -0.909,-0.416,-2)???

ganeshie8 · Answer

how did u get t = -2 ?

anonymous · Answer

-9:S

ganeshie8 · Answer

then ?

ganeshie8 · Answer

r(t) = <sin t, cos t, t >
r(-9) = ?