# How solve this equation where 0.8=0.2 cos (31.4 t) where 31.4 is the unit in radian per second and we want to find t (time)value, the answer is t=0.037 seconds, how to solve it algebraically?

Aug 15, 2015

Hi Shafiyah, you cannot really solve this equation because your function goes only from $0.2$ to $- 0.2$ (amplitude) and $0.8$ cannot be reached!

#### Explanation:

If you have $0.8$ you have:
$0.8 = 0.2 \cos \left(31.4 t\right)$
$\cos \left(31.4 t\right) = \frac{0.8}{0.2} = 4$ that cannot be ($\cos$ goes from $1$ to $- 1$ only!);

If it is: $0.08 = 0.2 \cos \left(31.4 t\right)$ then:
$\cos \left(31.4 t\right) = \frac{0.08}{0.2} = 0.4$
$31.4 t = a r \cos \left(0.4\right) = 1.1593$
$t = \frac{1.1593}{31.4} = 0.037 s$