Find the Exact Value tan(450)

Problem

tan(450)

Solution

1. Identify the angle and determine its coterminal equivalent within the standard range of 0 to 360 by subtracting 360

θ=450−360

θ=90

2. Apply the definition of the tangent function in terms of sine and cosine.

tan(90)=sin(90)/cos(90)

3. Substitute the known values for the sine and cosine of 90 from the unit circle.

sin(90)=1

cos(90)=0

4. Evaluate the resulting fraction. Since the denominator is zero, the expression is undefined.

tan(90)=1/0

Final Answer

tan(450)=undefined

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