Question

Use a graphing calculator to solve the equation -2sin(theta)= 1.2 in the interval from 0 to 2pi.

Answer 1

Answer:

$\theta=\pi +arcsin(\frac{3}{5})\approx 3.785\\\\\theta=2\pi -arcsin(\frac{3}{5} ) \approx 5.64$  

Step-by-step explanation:

As you can see from the graph I attached you, the possible solutions in the interval from 0 to 2π are approximately:

$\theta=3.7\\\\and\\\\\theta=5.7$

So, it's useful to solve the equation too, in order to verify the result:

$-2sin(\theta)=1.2\\\\sin(\theta)=-\frac{3}{5}$

Taking the inverse sine of both sides:

$\theta=\pi +arcsin(\frac{3}{5})\approx 3.785\\\\\theta=2\pi -arcsin(\frac{3}{5} ) \approx 5.64$

Using this result we can conclude the solutions in the interval from 0 to 2π are approximately:

$\theta\approx 3.785\\\\\theta \approx 5.64$