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?

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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?

1 Answer

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Answer 1 · 2015-08-15T14:29:25

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

Explanation:

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

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

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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?

1 Answer

Explanation:

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