Find the Exact Value tan(37 degrees )

Problem

tan(37)

Solution

1. Identify the task as finding the exact trigonometric value of tan(37)

2. Recognize that 37 is not a standard angle (like 30 45 or 60 typically found on the unit circle.

3. Relate the angle to the Pythagorean triple (3,4,5) In a right triangle with side lengths 3 4 and 5 the angle opposite the side of length 3 is approximately 36.87 which is often rounded to 37 in introductory physics and geometry contexts.

4. Apply the definition of the tangent ratio, which is the length of the opposite side divided by the length of the adjacent side.

5. Calculate the ratio using the side lengths 3 (opposite) and 4 (adjacent).

Final Answer

tan(37)=3/4

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