Find the Exact Value tan(pi/2)

Problem

tan(π/2)

Solution

1. Identify the definition of the tangent function in terms of sine and cosine.

tan(θ)=sin(θ)/cos(θ)

2. Substitute the given angle θ=π/2 into the definition.

tan(π/2)=sin(π/2)/cos(π/2)

3. Evaluate the sine and cosine values at π/2 using the unit circle.

sin(π/2)=1

cos(π/2)=0

4. Determine the result of the division by zero.

tan(π/2)=1/0

5. Conclude that since division by zero is not defined, the value does not exist.

tan(π/2)=undefined

Final Answer

tan(π/2)=undefined

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