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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