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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