Answer:
- 3rd quadrant: 210°
- 4th quadrant: 330°
Step-by-step explanation:
The equation can be rearranged by subtracting 1, then dividing by 2. Doing so gives you ...
... sin(x) = -1/2
The sine of an angle is the y-coordinate of the point where its terminal ray intersects the unit circle. A horizontal line at y=-1/2 intersects the unit circle in two places. (Refer to the attached diagram.) In each case, the reference angle (the smallest angle made with the x-axis) is 30°.
Conventionally, we measure angles counterclockwise from the +x axis, so the 3rd-quadrant angle (between 180° and 270°) will be 180°+30° = 210°.
The 4th-quadrant angle (between 270° and 360°) will be 360°-30° = 330°.
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Comment on the diagram
The geometry program used to create the figure decided to show the angles measured clockwise. To get the answers you want, you need to subtract the angles shown from 360°.
Comment on calculator solutions
If you use a calculator (in degrees mode) to find the angle whose sine is -1/2, it will tell you sin⁻¹(-0.5) is -30°. This means the angle is 30° measured clockwise from the +x axis. Of course, the value you want in that quadrant is 360°-30° = 330°. You have to understand that the third quadrant angle can be found by adding the reference angle (30°) to 180°.
