Question

Which of the following is true of the location of an angle, Theta, whose tangent value is Negative StartFraction StartRoot 3 EndRoot Over 3 EndFraction? Theta has a 30-degree reference angle and is located in Quadrant II or IV Theta has a 30-degree reference angle and is located in Quadrant II or III Theta has a 60-degree reference angle and is located in Quadrant II or IV Theta has a 60-degree reference angle and is located in Quadrant II or III.

Answer 1

The value of theta has a 30-degree reference angle and is located in Quadrant II or IV.

Given to us

$tan \theta =-\dfrac{\sqrt{3}}{3}$

What is the value of $tan \theta =\dfrac{\sqrt{3}}{3}$?

To know the value  $tan \theta =\dfrac{\sqrt{3}}{3}$ we will simplify the given expression,

$tan \theta =\dfrac{\sqrt{3}}{3}\\\\\\tan \theta =\dfrac{1}{\sqrt{3}}\\\\tan \theta =30^o$

Hence, the value of theta is 30°.

Finding the location of the - tan30°?

To know that the location of the -tan30°,

$tan30^o = -\dfrac{sin30^o}{cos30^o}$

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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