Find the Exact Value tan(780)

Problem

tan(780)

Solution

1. Find the coterminal angle by subtracting multiples of 360 until the angle is within the range [0,360)

780−2*(360)=780−720

780−720=60

2. Apply the periodic property of the tangent function, which states that tan(θ+n⋅360)=tan(θ)

tan(780)=tan(60)

3. Identify the exact value of the tangent function at 60 using the unit circle or a special right triangle (30−60−90.

tan(60)=√(,3)

Final Answer

tan(780)=√(,3)

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