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deliriwmfg

Answered question

2021-11-10

Find the terminal point P(x, y) on the unit circle determined by the given value of t.

t = \frac{7 π}{6}

Answer & Explanation

Alfonso Miller

Beginner2021-11-11Added 20 answers

The coordinates of the terminal point P(x, y) calculated by $t = \frac{7 π}{6}$ , we can find its reference angle.
$t = \frac{7 π}{6}$ lies in Quadrant lll, so its reference angle is its distance from the negative x-axis. The negative x-axis is an angle of $π$ so the reference angle is:
$\overset{―}{t} = \frac{7 π}{6} - π = \frac{π}{6}$
The angle $\overset{―}{t} = \frac{π}{6}$ has a terminal point of $Q (\frac{\sqrt{3}}{2}, \frac{1}{2})$ .
Since P lies in Quadrant lll, it has negative x- and y-coordinates. Negating the coordinates of Q then gives
$P (- \frac{\sqrt{3}}{2}, - \frac{1}{2})$
Answer: $P (- \frac{\sqrt{3}}{2}, - \frac{1}{2})$

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