Tangent Functions

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Definition

The figure is a unit circle, with origin O as centre cuts the x-axis at A (1,0) and let a variable point moving on the circumference move through an arc length q. i.e., AP = p(q). The coordinates at the position of p(q) are p(x,y) = (cos q, sin q).

Then the tangent function is defined in the form as

Sign of the value of the trigonometric function

The figure shows the position of the variable point A along the circumference of the unit circle. When it is at P₁, Q₁, R and S making angle q with the x-axis