contestada

Which of the following is true of the location of an angle, theta, whose tangent value is -sqrt3/3?
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

Respuesta :

calculista
Let
x-------> the angle theta

we know that
tan x=sin x/cos x

if  [tex]tan x= - \frac{ \sqrt{3} }{3} [/tex]

then
x belongs to the II quadrant or IV quadrant

sin 30°=[tex] \frac{1}{2} [/tex]
cos 30°=[tex] \frac{ \sqrt{3} }{2} [/tex]

therefore
tan 30°=[tex] \frac{ \sqrt{3} }{3} [/tex]

Hence
the angle theta has a 30-degree reference angle and is located in Quadrant II or IV
abidemiokin

Theta has a 30-degree reference angle and is located in Quadrant II or IV

Given the trigonometry value expressed as:

  • [tex]tan \theta = -\frac{\sqrt{3}}{3}[/tex]

Calculate the reference angle as shown:

[tex]\theta = arctan(\frac{\sqrt{3}}{3} )\\\theta = -30^0[/tex]

According to the quadrant, the value of tan is negative in the 2nd and the fourth quadrant. Hence the true statement will be theta has a 30-degree reference angle and is located in Quadrant II or IV

Learn more on trigonometry here: https://brainly.com/question/19800786