Find the Exact Value tan(37)

Problem

tan(37^∘)

Solution

1. Identify the expression as the tangent of 37 degrees.

2. Determine if 37^∘ is a standard angle on the unit circle. Since 37^∘ is not one of the common reference angles (such as 0^∘,30^∘,45^∘,60^∘,90^∘, its exact value cannot be expressed using simple radicals or integers.

3. Recognize that 37^∘ is often used in physics as an approximation for the smaller angle in a 3−4−5 right triangle, where tan(36.87^∘)≈3/4 However, for the exact mathematical value of tan(37^∘) the expression remains in its trigonometric form.

Final Answer

tan(37^∘)=tan(37^∘)

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