Find the Exact Value tan(53)

Problem

tan(53^∘)

Solution

1. Identify the given expression as the tangent of an angle measured in degrees, tan(53^∘)

2. Determine if the angle is a standard reference angle (such as 30^∘ 45^∘ or 60^∘. Since 53^∘ is not a standard reference angle, its exact value cannot be expressed using simple radicals or integers.

3. Recognize that 53^∘ is often used in physics as an approximation for the larger acute angle in a 3−4−5 right triangle, where tan(53.13^∘)≈4/3

4. Conclude that without further trigonometric identities or specific approximations, the exact value is simply written as the function itself.

Final Answer

tan(53^∘)=tan(53^∘)

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