Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Sample Practice Questions (3)

In the coordinate plane, a unit circle is centered at the origin. If an angle

θ = \frac{π}{3}

is in standard position, what are the coordinates of the point where the terminal side of the angle intersects the unit circle?

(\frac{1}{2}, \frac{3}{2})

(\frac{3}{2}, \frac{1}{2})

(\frac{2}{2}, \frac{2}{2})

(0, 1)

On the unit circle, an angle of

θ = \frac{π}{6}

radians is in standard position. What are the coordinates of the point where the terminal side of the angle intersects the circle?

(\frac{3}{2}, \frac{1}{2})

(\frac{1}{2}, \frac{3}{2})

(\frac{2}{2}, \frac{2}{2})

(1, 0)

What is the reference angle for

θ = \frac{11 π}{6}

\frac{π}{6}

\frac{π}{3}

- \frac{π}{6}

\frac{5 π}{6}

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