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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