The tangent of the given angles are the ratios y to the x coordinate of
the point of the terminal side on the unit circle.
The correct options are;
The tangent of an angle is given as follows;
[tex]tan (\theta) = \mathbf{ \dfrac{Opposite}{Adjacent}} = \dfrac{\Delta y}{\Delta x}[/tex]
First angle
An angle given is; [tex]\mathbf{\dfrac{34 \cdot \pi}{3}}[/tex]
Therefore;
[tex]tan \left(\dfrac{34 \cdot \pi }{3} \right) = \mathbf{ \sqrt{3}}[/tex]
The above result can be obtained as follows;
[tex]\sqrt{3} = \mathbf{ \dfrac{-\dfrac{\sqrt{3} }{2} }{-\dfrac{1}{2} }}[/tex]
Which is obtained when we have;
[tex]\left( \Delta x, \, \Delta y\right) = \mathbf{\left(-\dfrac{1}{2}, \, -\dfrac{\sqrt{3} }{2} \right)}[/tex]
Therefore
The required coordinates is therefore;
Second angle
The angle, [tex]\mathbf{-\dfrac{7 \cdot \pi}{4}}[/tex], gives; [tex]tan \left(-\dfrac{7 \cdot \pi}{4} \right) = 1[/tex]
The above value can be obtained as follows;
[tex]\mathbf{\dfrac{\dfrac{\sqrt{2} }{2} }{\dfrac{\sqrt{2} }{2} }} = 1[/tex]
Which gives;
Third angle
The angle 210° gives; tan(210°) = [tex]\mathbf{\frac{1}{\sqrt{3} }}[/tex], which can be obtained as follows;
[tex]\sqrt{ \dfrac{1}{3} } = \mathbf{\dfrac{-\dfrac{1}{2} }{-\dfrac{\sqrt{3} }{2} }}[/tex]
Therefore;
Learn more about the unit circle here:
https://brainly.com/question/1673530
