Particle in Positive Direction

[Painguy]

Homework Statement

d) When is the particle moving in the positive direction?
$f(t) = cos(πt/4), t ≤ 10$

Homework Equations

$f '(t) = -(π/4)sin(π(t)/4)$

The Attempt at a Solution

$0 < -(π/4)sin(π(t)/4)$

$(π(t)/4)>πn$

$t>4n 0<=n<=2$

$t>4 t>8$


The answer says 8>t>4

im probably skipping a simple step. wut do?

 

[Mark44]

Homework Statement

d) When is the particle moving in the positive direction?
$f(t) = cos(πt/4), t ≤ 10$

Homework Equations

$f '(t) = -(π/4)sin(π(t)/4)$

The Attempt at a Solution

$0 < -(π/4)sin(π(t)/4)$

So after multiplying both sides by -4/π, you get sin(πt/4) < 0.
Sketch a graph of y = sin(πt/4) and you'll see that 4 < t < 8 is indeed the interval.

I don't get what you did to arrive at the inequality below.

$(π(t)/4)>πn$

$t>4n 0<=n<=2$

$t>4 t>8$


The answer says 8>t>4

im probably skipping a simple step. wut do?