Find the Exact Value cot(80)

Problem

cot(80^∘)

Solution

1. Identify the expression as the cotangent of an angle measured in degrees.

2. Recognize that 80^∘ is not a standard reference angle (like 30^∘ 45^∘ or 60^∘, so the exact value is typically expressed in terms of trigonometric functions of standard angles or left in its simplest trigonometric form.

3. Apply the cofunction identity cot(θ)=tan(90^∘−θ) to rewrite the expression.

4. Substitute θ=80^∘ into the identity.

90^∘−80^∘=10^∘

5. Simplify the expression to its equivalent tangent form.

cot(80^∘)=tan(10^∘)

Final Answer

cot(80^∘)=tan(10^∘)

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