Respuesta :
The value of theta has a 30-degree reference angle and is located in Quadrant II or IV.
Given to us
[tex]tan \theta =-\dfrac{\sqrt{3}}{3}[/tex]
What is the value of [tex]tan \theta =\dfrac{\sqrt{3}}{3}[/tex]?
To know the value [tex]tan \theta =\dfrac{\sqrt{3}}{3}[/tex] we will simplify the given expression,
[tex]tan \theta =\dfrac{\sqrt{3}}{3}\\\\\\tan \theta =\dfrac{1}{\sqrt{3}}\\\\tan \theta =30^o[/tex]
Hence, the value of theta is 30°.
Finding the location of the - tan30°?
To know that the location of the -tan30°,
[tex]tan30^o = -\dfrac{sin30^o}{cos30^o}[/tex]
As the value is negative, therefore, there can be two cases,
Case I: when the value of Sin30° is negative,
Case II: when the value of cos30° is negative.
Case I: when the value of Sin30° is negative,
If the value of Sin30° is negative, while the value of cos30° is positive, the θ will lie in the fourth quadrant.
Case II: when the value of Cos30° is negative,
If the value of Cos30° is negative, while the value of Sin30° is positive, the θ will lie in the second quadrant.
Hence, the value of theta has a 30-degree reference angle and is located in Quadrant II or IV.
Learn more about Quadrants:
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