Have you ever wondered if a "tangent line" in Geometry has any relation to the "tangent of an angle" in trigonometry?[br]Or "secant line" and "secant of an angle?"[br]What relation is implied by the prefix "co-" when discussing sine and cosine, tangent and cotangent, or secant and cosecant?[br](Did you know it has to do with "complementary" angles?)[br]This worksheet is intended to help students see such connections.
Drag the red point along the circumference of the unit circle, observing the changes in the various line segments.[br]Toggle on/off the various checkboxes and adjust the slider.[br]In Geometry, what does it mean for a line or line segment to be tangent to a circle?[br]In Geometry, what does it mean for a line or line segment to be secant to a circle?[br]Thinking of the Geometry definitions, why are the terms "tangent" and "secant" appropriate for labeling the respective line segments on the unit circle?[br]Referencing the unit circle, why is tan(theta) equal to the quotient of sin(theta)/cos(theta)?[br]In the unit circle what angle is formed by the line segments representing sine and cosine?[br]In the unit circle what angle is formed by the line segments representing tangent and cotangent?[br]There are several similar/proportional right triangles on the unit circle at any time (Except arguably the case when theta is a "quadrantal" angle). Using proportions, explain why any trig function(theta) = cofunction(complement of theta). In other words,[br]* sine(theta) = cosine(complement of theta) for all values of theta[br]* tangent(theta) = cotangent(complement of theta) for all values of theta[br]* secant(theta) = cosecant(complement of theta) for all values of theta