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)&gt;πn

t&gt;4n 0&lt;=n&lt;=2

t&gt;4 t&gt;8


The answer says 8>t>4

im probably skipping a simple step. wut do?