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Answer:

The terminal point of 7pi/6 is [tex](-\frac{\sqrt{3}}{2}-\frac{1}{2})[/tex].

Step-by-step explanation:

We need to find the terminal points of 7pi/6.

In a unit circle, the terminal point of θ is defined as

[tex](r\cos \theta,r\sin \theta)[/tex]

where, r is the radius of the circle.

Let as assume we need to find the terminal points of 7pi/6 for a unit circle.

[tex]\theta=\frac{7\pi}{6}[/tex] and r=1

Substitute these values in the above formula.

[tex]((1)\cos (\frac{7\pi}{6}),(1)\sin(\frac{7\pi}{6}))[/tex]

[tex](\cos (\pi+\frac{\pi}{6}),\sin(\pi+\frac{\pi}{6}))[/tex]

[tex](-\cos (\frac{\pi}{6}),-\sin(\frac{\pi}{6}))[/tex]

[tex](-\frac{\sqrt{3}}{2}-\frac{1}{2})[/tex]

Therefore, the terminal point of 7pi/6 is [tex](-\frac{\sqrt{3}}{2}-\frac{1}{2})[/tex].
  • The circle unit Terminal Points in the unit circle to locate the terminal point, begin with (1,0).
  • When we calculating the degree of angle or radius mostly on the circle which moves clockwise.
  • The positive angle and the clockwise when the negative angle.
  • The final point is referred to as the endpoint coordinate.
  • Calculating the terminal points of [tex]\bold{\frac{7\pi}{6}}[/tex].
  • The end-point of [tex]\bold{\theta}[/tex] is specified as a unit circle.

[tex]\to \bold{(r \cos \theta, r \sin \theta)}[/tex]

Where r is the circle's radius.

Suppose that we have to discover [tex]\bold{\frac{7\pi}{6}}[/tex] terminal points for a unit circle.

[tex]\to \bold{\theta =\frac{7\pi}{6}} \\\\\to \bold{r=1}[/tex]

Substituting the value in the above formula:

[tex]\to \bold{((1) \cos \frac{7\pi}{6}, (1) \sin \frac{7\pi}{6} )}\\\\\to \bold{(\cos (\pi +\frac{\pi}{6}), \sin (\pi +\frac{\pi}{6} ))}\\\\\to \bold{(-\cos (\frac{\pi}{6}), -\sin (\frac{\pi}{6} ))}\\\\\to \bold{(-\frac{\sqrt{3}}{2},-\frac{1}{2})}[/tex]

Therefore, the terminal point of   is

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