You convert by adding the equivalent of a circle, either 360 degrees or 2 pi radians.
So converting - 0.848 radians to positive radian measure gives you what?
And 2A equals that number so A equals?
Now, when I explained about the arcsin, I said that it had a limited domain. It only gives answers for angles in the first and fourth quadrant. In what quadrants is the sine function negative and so possibly equal to - 0.75?
4 sin 2A= -3, for 0 ≤ A ≤ 2 Pi radians Answer = 1.99 and 2.72
converting 2A to positive (6.28 + . 8.48) = 7.128 pi
the sin function is negative in the 4th quadrants , i still no were near find out how i get the answer could you show me the steps involved please as i have no example to follow !!
Step 1.
$4sin(2A) = - 3 \implies sin(2A) = \dfrac{-\ 3}{4} = -\ 0.75.$ Obvious.
Step 2. I want an answer in positive radians so I calculate in radians.
$sin(2A) = -\ 0.75 \implies 2A = arcsin(-\ 0.75) \approx -\ 0.84806\ radians.$ This just requires setting up a scientific calculator in radians.
Step 3.
The answer we got in step 2 is in negative radians and because $-\ \dfrac{\pi}{2} \approx -\ 1.571 < -\ 0.848$
the answer is in the fourth quadrant. That means there is no answer in quadrant I. There cannot be an answer in quadrant II because the sine is positive in that quadrant. But there will be a second answer in quadrant III because the sine will be negative there. The arcsine function only gives answers for the first and fourth quadrants.
Let's deal with quadrant IV first.
$2A \approx -\ 0.84806\ radians \implies 2A = (-\ 0.84806 + 2\pi)\ radians = 5.43513\ radians \implies A = \dfrac{5.43513\ radians}{2} \approx 2.72\ radians.$
That was one answer given to you.
Step 4
There are various ways to proceed to find the other solution. They all involve moving around the unit circle. We saw that
$sin(-\ 0.84806) = -0.75 \implies sin(0.84806) = 0.75$, which puts us into Quadrant I. To get to Quadrant III, add pi radians.
$0.84806 + \pi \approx 3.989653.$ Let's check: $sin(3.989653) \approx -\ 0.75.$
So $2A = 3.989653 \implies A = \dfrac{3.989653}{2} = 1.99.$ That was the other answer.
This problem involves understanding what the inverse trig functions do and how to move around the unit circle.