Question

If $\sin \left(\mathrm{x}\right)=0.7$, how do you list all possible values of $x.\mathrm{if}-180<x<180$?

Answer 1

Finding the value of $\mathrm{x}$ in the range of $\left(-180,180\right)$ .

Given,$\sin \left(\mathrm{x}\right)=0.7$

Taking ${\sin }^{-1}$ both sides:
$\begin{array}{rcl}{\sin }^{-1}\sin \left(x\right)& =& {\sin }^{-1}(0.7)\\ & \Rightarrow & x=44.42\end{array}$
The trig unit circle gives another arc$\mathrm{x}=180-44.42=135.58\mathrm{deg}$.

which has the same value $\sin \left(\mathrm{x}\right)=0.7$ within the interval$\left(-180,180\right)$,

Hence, there is two possible value of $x$ in the given range ${\mathrm{x}}_1=44.42\mathrm{deg}\mathrm{and}{\mathrm{x}}_2=135.58\mathrm{deg}$.