Question

Can someone please help me and write out the answer​

Answer 1

9514 1404 393

Answer:

  -30°

  or 330° or -150° or 210°

Step-by-step explanation:

The angle whose sine is 1/2 is 30°. Here, the sine is negative, indicating the angle is in the 3rd or 4th quadrants.

The angles in those quadrants with a reference angle of 30° are -30° or -150°. As positive angles, these are 330° or 210°, respectively.

Generally, the sin⁻¹ function (also called the arcsin function) is defined to have a range of -90° to +90°. Within that range, we can say ...

  sin⁻¹(-1/2) = -30°

_____

Additional comment

There are a few trig functions it is worthwhile to remember. These are shown in the attachment. The ordered pair points on the unit circle are (cos(θ), sin(θ)). If you remember the values of these in the first quadrant for 30°, 45°, and 60°, then you can work most of these "without a calculator" problems. (You also need to know how the signs change in the different quadrants.)

Answer 2

Answer:

210 degrees

Step-by-step explanation:

This is the 'arcsin' or 'inverse sine' function.  As written,

arcsin (-1/2) is requesting the angle (in degrees) whose sine is -1/2.

Note that because the sine function is defined as (opposite side)/hypotenuse, the following equation is true:

 -1            opposite

------  =  -------------------  =  sin x, where x is an angle in degrees.

  2         hypotenuse

If the sine is negative, that means that the angle x lies in either Quadrant III or Quadrant IV.  We see that the magnitude of the opposite side is HALF the magnitude of the hypotenuse.  

Cycling counterclockwise from the positive x axis, and continuing through Quadrant II into Quadrant III, we get a ray (hypotenuse) that is twice the length of the opposite side.  The angle of this ray as measured from the positive x-axis is 180 degrees plus 30 degrees, or  210 degrees.

You can check this by finding sin 210° on a calculator; the result is -1/2, which is what we were given up front.