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​The Unit Circle

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Using the Unit Circle

• To use the Unit Circle to evaluate cosine, sine, or tangent we use the coordinates of the point of intersection between the terminal side of the angle and the Unit Circle.

• The x-coordinate of the point is equal to the cosine of the angle.

• The y-coordinate of the point is equal to the sine of the angle.

• To find the tangent of an angle you take the y-coordinate/x-coordinate.

Evaluate Tangent

• Tan(angle) = y-coordinate/x-coordinate tanΘ=opp/adj

• Tangent is positive in the FIRST and THIRD quadrants.

• Tangent is negative in the SECOND and FOURTH quadrants.

• tan(90°) = 1/0 = UNDEFINED

• tan(π) = 0/-1 = 0

• tan(240°) = (-√3/2)/(-1/2)

• =(-√3/2) *(-2/1) = √3/1 = √3Θ

Multiple Choice

Point R(3, 4) is a point on the terminal side of the angle $$\theta$$ . Find the exact value of tangent $$\theta$$ . #41

• $$\frac{3}{4}$$  

• $$-\frac{4}{3}$$  

• $$\frac{4}{5}$$  

• $$\frac{4}{3}$$  

Multiple Choice

Point Q(-5, -12) is a point on the terminal side of the angle $$\theta$$ . Find the exact value of cosine $$\theta$$ . #42

• $$\frac{5}{13}$$  

• $$-\frac{12}{13}$$  

• $$-\frac{5}{13}$$  

• $$-\frac{13}{5}$$