Answer:
The sign of the trigonometric ratio only aid you to determine the quadrant in which the ratio lies.
Step-by-step explanation:
Given [TeX]sin \theta=- \frac{1}{2}[/TeX]
[TeX]\theta \neq -30[/TeX]
The trigonometric ratio sine is negative in the 3rd and 4th Quadrant. Therefore if [TeX]sin \theta=- \frac{1}{2}[/TeX], the value(s) of [TeX]\theta [/TeX] in the interval [0,360°) will be in the 3rd and 4th Quadrant.
To obtain the value of [TeX]\theta [/TeX] in these quadrants:
Solve for [TeX]sin \theta=\frac{1}{2}\\sin^{-1}\frac{1}{2}=30^{0}[/TeX]
In the 3rd Quadrant, [TeX]\theta =180+30=210^{0} [/TeX]
In the 4th Quadrant, [TeX]\theta =360-30=330^{0} [/TeX] .
The sign of the trigonometric ratio only aid you to determine the quadrant in which the ratio lies.
