# Math Help - finding solutions for cos

1. ## finding solutions for cos

I have to find the two solutions for;

$
cos(2t)=-0.75, \pi < t < 2 \pi
$

i have sketched a graph, but am unsure how to get the values mathematically?

Many thanks

2. Originally Posted by madmax29
I have to find the two solutions for;

$
cos(2t)=-0.75, \pi < t < 2 \pi
$

$\pi < t < 2\pi$

$2\pi < 2t < 4\pi$

$\cos(2t) = -0.75$

$2t = 2\pi + \arccos(-0.75)$

$t = \pi + \frac{1}{2}\arccos(-0.75)$

$2t = 4\pi - \arccos(-0.75)$

$t = 2\pi - \frac{1}{2}\arccos(-0.75)$

3. the question then goes on to say, "if the solutions are denoted by t1 and t2 where t1 < t2, find t1 and t2?"

what are the answers?

4. Originally Posted by madmax29
the question then goes on to say, "if the solutions are denoted by t1 and t2 where t1 < t2, find t1 and t2?"

what are the answers?
you can't tell which solution for t is the largest or smallest?

5. is it 8.70 rads & 10.15 rads, or 4.35 rads & 5.07 rads????

6. Originally Posted by skeeter
you can't tell which solution for t is the largest or smallest?
i can, but i need to know which range, both seems to satisfy the t1 < t2 criteria??? but which is which, if you see what i mean?

7. one more time ...

$t = \pi + \frac{1}{2}\arccos(-0.75)$

$t = 2\pi - \frac{1}{2}\arccos(-0.75)$

evaluate each value of t in your calculator ... check the results with your graph.

8. so because the summary of the statement is a just a $t$ as apposed to $2t$, then the ones with $t$ are the real answers? would this statement be correct?

9. Originally Posted by madmax29
so because the summary of the statement is a just a $t$ as apposed to $2t$, then the ones with $t$ are the real answers? would this statement be correct?
The answer has been given - twice. You are asked to solve for t.