Simplify tan(40)

Problem

tan(40^∘)

Solution

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

2. Determine if the angle is a standard reference angle. The angle 40^∘ is not one of the standard angles (like 0^∘ 30^∘ 45^∘ 60^∘ or 90^∘ that have exact radical forms for trigonometric functions.

3. Recognize that without a specific identity or a calculator, the expression tan(40^∘) is already in its simplest exact trigonometric form.

4. Approximate the value using a calculator if a decimal representation is required.

Final Answer

tan(40^∘)≈0.8391

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