# Math Help - (a) "Evaluate h(t) = cos (20t)° for t = 3." (b) What is the value of t when h(t) =...

1. ## (a) "Evaluate h(t) = cos (20t)° for t = 3." (b) What is the value of t when h(t) =...

Hi there, doing some 11th grade trig I've run into difficulty. Here are the questions I'm having trouble with:

(a) Evaluate h(t) = cos (20t)° for t = 3.
(b) What is the value of t when h(t) = 0.3 for 0 ≤ t ≤ 18?

(a) 1/2
(b) 3.6, 14.4

For (a), I get 1/2 no problem, which the book lists as the correct answer. But for (b), I only understand how to get 3.6 and not 14.4 - conceptually and practically, I'm not following how to get the 14.4 beyond a vague idea that this involves periodic values of the function.

If you could point me in the right direction or give me a similar problem with the solution and steps for that problem, I'd really appreciate it.

Thanks

2. ## Re: (a) "Evaluate h(t) = cos (20t)° for t = 3." (b) What is the value of t when h(t)

if $0 \le t \le 18$ , then $0 \le 20t \le 360$

let $u = 20t$

$\cos(u) = 0.3$

since cos(u) = 0.3 , there is one solution in quad I and one solution in quad IV (cosine is positive in quads I and IV). note that the inverse cosine function (arccos) has a range from 0 to 90 degrees for positive values of cosine, so ...

$u = \arccos(0.3) \approx 72.5^\circ$

$u = 360 - \arccos(0.3) \approx 287.5^\circ$

divide each angle above by 20 to get the values for t between 0 and 18.