To determine the sign (+ or -) of the tangent and cotangent, multiply the length of the tangent by the signs of the x and y axis intercepts of that “tangent” line you drew. If you extend the tangent line to the y-axis, the distance of the line segment from the tangent point to the y-axis is the cotangent (COT). The distance of this line segment from its tangent point on the unit circle to the x-axis is the tangent (TAN). This line is at right angles to the hypotenuse at the unit circle and touches the unit circle only at that point (the tangent point). Using the unit circle diagram, draw a line “tangent” to the unit circle where the hypotenuse contacts the unit circle. I do not understand why Sal does not cover this. While you are there you can also show the secant, cotangent and cosecant. I think the unit circle is a great way to show the tangent.
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