trying to find t where 6=sinh^2/3(4t), i'm struggling to understand the inverse of sinh when the power isn't one
Solve for t:
6 = 4 t (sinh(x))^(1/3)^2
4 t (sinh(x))^(1/3)^2 = 4 t sinh^(2/3)(x):
6 = 4 t sinh^(2/3)(x)
6 = 4 t sinh^(2/3)(x) is equivalent to 4 t sinh^(2/3)(x) = 6:
4 t sinh^(2/3)(x) = 6
Divide both sides by 4 sinh^(2/3)(x):
Answer: | t = 3/(2 sinh^(2/3)(x))
+9466 Can you first raise both sides to the 3/2 power...then take the sinh inverse of both sides?
Like this:
\(6=\sinh^{\frac23}(4t) \\~\\ \\~\\ 6^{\frac32}=\sinh^{\frac23*\frac32}(4t) \\~\\ 6\sqrt{6}=\sinh(4t) \\~\\ \sinh^{-1}(6\sqrt{6})=4t \\~\\ \frac{\sinh^{-1}(6\sqrt{6})}{4}=t \\~\\ t \approx 0.845 \text{ radians} \\ t \approx 48.443 \text{ degrees}\)
Assuming that was the question.
It took me awhile to check this because in most calculators you need to input it like this:
[sinh(4(0.845))]^(2/3) 
*edited to clarify that it is 0.845 radians, and to add degrees.*
