options: 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.

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.

Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
problem_activity: Draw and label a figure on the circle that illustrates the relationship of the trigonometric tangent functions
$${\mathrm{tan}=\frac{\mathrm{sin}(\theta^\circ)}{\mathrm{cos}(\theta^\circ)}}$$
and the geometric tangent line to a circle through the point
$${(1,0)}$$
when
$${\theta=60}$$
. Explain the relationship, labeling the figure as needed.
[IMG]


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