1. ## Re: Trigonometry im lost

Originally Posted by derm
I don't know how to do it!! It = convert from negative measure of an angle to positive measure
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?

2. ## Re: Trigonometry im lost

Originally Posted by Plato
The answer i got is 1.99 and 2.72 , the link is a bit confusing

3. ## Re: Trigonometry im lost

Originally Posted by JeffM
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 !!

4. ## Re: Trigonometry im lost

Originally Posted by derm
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.

$sin(2A) = -\ 0.75 \implies 2A = arcsin(-\ 0.75) \approx -\ 0.84806\ radians.$ 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 $-\ \dfrac{\pi}{2} \approx -\ 1.571 < -\ 0.848$

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.

5. ## Re: Trigonometry im lost

That is a step by step solution.

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