# Thread: finding solutions for cos

1. ## finding solutions for cos

I have to find the two solutions for;

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

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

Many thanks

I have to find the two solutions for;

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

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

$\displaystyle \cos(2t) = -0.75$

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

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

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

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

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

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

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

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 ...

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

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

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 $\displaystyle t$ as apposed to $\displaystyle 2t$, then the ones with $\displaystyle t$ are the real answers? would this statement be correct?

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