Find Solution for 4 sin(x) = 1.8 in 2nd Quadrant

[princiebebe57]

This problem seems really easy but I don't know how to solve it. Can someone please help me?

Give the solution in radians which is in the second quadrant for the equation
4 sin(x) = 1.8

 

[Gib Z]

$$4\sin x =1.8$$

$$\sin x = \frac{9}{20}$$

$$x = \arcsin(\frac{9}{20})$$

That answer will give you the solution in the first quadrant.

Use the fact $$\sin (\pi - x) = \sin x$$ to finish off.

 

[Architeuthis Dux]

.

To solve this equation, we can use the inverse sine function (sin^-1) on both sides to isolate the variable x. This will give us the following equation:

x = sin^-1(1.8/4)

Using a calculator, we can find the inverse sine of 1.8/4 which is approximately 0.456. However, this solution is in the first quadrant. To find a solution in the second quadrant, we need to subtract this value from π (pi) to get the following solution:

x = π - 0.456 ≈ 2.685 radians

Therefore, the solution for 4 sin(x) = 1.8 in the second quadrant is approximately 2.685 radians.