I. Graphing the Tangent Function • The tangent of an angle is derived from the coordinates of a point on a line that is tangent to a circle. • Tangent θ – the y – coordinate of the point where the line containing the terminal side of the angle intersects the tangent line x = 1.
THINK: TANGENT = OPPOSITE/ADJACENT • Therefore, the tangent is equal to sin/cos
Notice as you graph the tangent function it, approaches infinity, and thus has asymptotes at specified values.
II. Properties of y = a tan b θ • There is no amplitude • Once cycle occurs in the interval from (-π/2b) to (π/b) π/b is the period of the function there is vertical asymptotes at each end of the cycle
Example 1: graph the following: • A) y = 50 tan θ • B) f(x) = tan (π/6)θ
Example 2: solve the following: • A) tan θ = 2 • B) 6 tan θ = 1