Parametric equations, and a helix

[FizzyCrow]

I have a question here that is bugging me!! Thanks for any info


Find the parametric equations for the line tangent to the helix r=(sqr2 cos(t))i+(sqr2 sin(t)j+tk at the point where t=pi/4.

 

[soroban]

Hello, FizzyCrow!

Find the parametric equations for the line tangent to the helix
r = (√2·cos(t))i + (√2·sin(t)j + tk at the point where t = π/4.

When t = π/4, the point is: . [√2·cos(π/4)]i + [√2·sin(π/4)j + (π/4)k .= .(1, 1, π/4)


The derivative is: .r' .= .[-√2·sin(t)]i + [√2·cos(t)]j + k

. . When t = π/4: .r' .= .[-√2·sin(π/4)]i + [√2·cos(π/4)]j + k .= .[-1, 1, 1]


The parametric equations are: .x .= .1 - t, . y .= .1 + t, . z .= .π/4 + t