Posted by **abby** on Friday, April 16, 2010 at 6:43pm.

At what points does the helix r = sin(t), cos(t), t intersect the sphere x^2 + y^ 2 + z^2 = 26?

(Round your answers to three decimal places. Enter your answers from smallest to largest z-value.)

- Calculus -
**MathMate**, Friday, April 16, 2010 at 7:31pm
The sphere, S, is given by:

S(x,y,z): x²+y²+z²-26=0

The helix, r, is given by:

r(x,y,z): sin(t),cos(t),t

which means that the helix is constrained to the cylinder of unit radius, C: C(x,y): x²+y²=1

Thus, the solution for the intersections is given by the solution of

S(sin(t), cos(t), t)=0

from which it can be deduced by inspection that t=5 gives an exact solution, since

(sin²(5)+cos²(5)) + 5²

=(1) + 25

=26

Similarly, t=-5 is a solution.

## Answer this Question

## Related Questions

calculus - At what points does the helix r = sin(t), cos(t), t intersect the ...

calculus - Solve the given equation. (Enter your answers as a comma-separated ...

precalculus - Use a Double- or Half-Angle Formula to solve the equation in the ...

pre-calc help - Solve the given equation. (Enter your answers as a comma-...

Calculus - Find the points of inflection of the curve below. Round the answers ...

precal - Solve the given equation. (Enter your answers as a comma-separated list...

Math Problem (please help) - Consider the following function. g(x) = 6x^4 −...

precalculus - If a projectile is fired with velocity v0 at an angle θ, then...

Calculus - Complete the table by computing f(x) at the given values of x. (Round...

precal - Solve the given equation. (Enter your answers as a comma-separated list...