2Slope on the Unit Circle What is the slope of the terminal side of an angle on the unit circle?1(cosӨ,sinӨ)sinӨOppositeӨ-1cosӨ1AdjacentUsing our knowledge of the Unit Circle…Or using trigonometry…Slope =-1
3A Definition of Tangent The tangent function is defined as:There are values for which the tangent function are undefined:Any Θ that makes cos(Θ)=0.
4Example Find the exact value of the following: Thought process The only thing required for a correct answer (unless the question says explain)
5The Tangent Function Graph XSIN(X)COS(X)-2π1-7π/40.707-3π/2-5π/4-0.707-π-1-3π/4-π/2-π/4π/4π/23π/4π5π/43π/27π/42πIn order to investigate the tangent function, first examine all the values of sine and cosine. Remember, tangent is sine divided by cosine.Now find and graph all of the values of sine÷cosine.
6The Tangent Function Graph XSIN(X)COS(X)-2π1-7π/40.707-3π/2-5π/4-0.707-π-1-3π/4-π/2-π/4π/4π/23π/4π5π/43π/27π/42πTAN(X)0/1 = 0.707/.707 = 11/0 = DNE.707/-.707 = -10/-1 = 0-.707/-.707 = 1-1/0 = DNE-.707/.707 = -1Find the values of sine divided by cosine.Plot the points.The errors are asymptotes.
7The Tangent Function Graph Domain: Range: AsymptotesAll Reals exceptAll Reals