Question

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

Answer 1

`\theta=\pi +arcsin((3)/(5))\approx 3.785\\\\\theta=2\pi -arcsin((3)/(5) ) \approx 5.64`

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)=-(3)/(5)`

Taking the inverse sine of both sides:

`\theta=\pi +arcsin((3)/(5))\approx 3.785\\\\\theta=2\pi -arcsin((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`