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The Tangent Function. Slope on the Unit Circle 1 1 Ө (cosӨ,sinӨ) cosӨ sinӨ Slope = Opposite Adjacent What is the slope of the terminal side of an angle.

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Presentation on theme: "The Tangent Function. Slope on the Unit Circle 1 1 Ө (cosӨ,sinӨ) cosӨ sinӨ Slope = Opposite Adjacent What is the slope of the terminal side of an angle."— Presentation transcript:

1 The Tangent Function

2 Slope on the Unit Circle 1 1 Ө (cosӨ,sinӨ) cosӨ sinӨ Slope = Opposite Adjacent What is the slope of the terminal side of an angle on the unit circle? Or using trigonometry… Using our knowledge of the Unit Circle…

3 A Definition of Tangent There are values for which the tangent function are undefined: The tangent function is defined as: Any Θ that makes cos(Θ)=0.

4 Example Find the exact value of the following: Thought process The only thing required for a correct answer (unless the question says explain)

5 The Tangent Function Graph In 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. XSIN(X)COS(X) -2π 01 -7π/ π/ π/ π-π 0 -3π/ π/2 0 -π/ π/ π/2 10 3π/ π 0 5π/ π/2 0 7π/ π2π 01

6 The Tangent Function Graph Find the values of sine divided by cosine. TAN(X) 0/1 = 0.707/.707 = 1 1/0 = DNE.707/-.707 = -1 0/-1 = /-.707 = 1 -1/0 = DNE -.707/.707 = -1 0/1 = 0.707/.707 = 1 1/0 = DNE.707/-.707 = -1 0/-1 = /-.707 = 1 -1/0 = DNE -.707/.707 = -1 0/1 = 0 Plot the points.The errors are asymptotes. XSIN(X)COS(X) -2π 01 -7π/ π/ π/ π-π 0 -3π/ π/2 0 -π/ π/ π/2 10 3π/ π 0 5π/ π/2 0 7π/ π2π 01

7 The Tangent Function Graph Domain: Range: Asymptotes All Reals except All Reals

8 Graph of Tangent (For 0 ≤ x ≤ 2 π )


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