Find the Exact Value tan(420)

Problem

tan(420)

Solution

1. Find the coterminal angle by subtracting 360 from the given angle to find an equivalent angle within the first rotation.

θ=420−360

θ=60

2. Identify the trigonometric identity for the tangent of a coterminal angle, which states that tan(θ+360⋅n)=tan(θ)

tan(420)=tan(60)

3. Determine the exact value of tan(60) using the properties of a 30−60−90 reference triangle or the unit circle.

tan(60)=√(,3)

Final Answer

tan(420)=√(,3)

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