Question

Solve sin(x)= -.036 on the interval 0 is less than or equal to x which is less than 2pi

Answer 1

In the interval

`0\leq x<2\pi`

We have two values that sin is negative. I will draw a trigonometric circle:

We can find these values using a calculator.

`x\text{ = }\sin ^(-1)(-0.36)`

This will give -21.1 degrees. If we start counting from zero, one complete circle is 360 degrees. So to find x2 we have to do:

`x2\text{ = 360 - 21.1 = 339 degr}ees`

And to find x1 we have to add 21.1 degrees counting from the start that is now 180:

`x1=180+21.1\text{ = 201.1 degre}es`

We do this process because we have two angles that give the same sin value, and they are symmetric compared to the sin axis!