Formula Used:
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This trigonometric formula expresses the tangent of an angle A in terms of the tangent of one-third of that angle. It's derived from triple-angle trigonometric identities and is useful in various mathematical and engineering applications.
The calculator uses the formula:
Where:
Explanation: This formula allows calculation of the tangent of the full angle when only the tangent of one-third of the angle is known.
Details: Trigonometric calculations are fundamental in mathematics, physics, engineering, and computer graphics. They help solve problems involving angles, distances, and periodic phenomena.
Tips: Enter the value of tan(A/3) in the input field. The calculator will compute and display the value of tan A. Note that the result may be undefined if the denominator equals zero.
Q1: When is this formula particularly useful?
A: This formula is useful in trigonometric simplifications, solving trigonometric equations, and in applications where angles are divided into equal parts.
Q2: What are the limitations of this formula?
A: The formula becomes undefined when the denominator equals zero, which occurs when \( \tan(A/3) = \pm \frac{1}{\sqrt{3}} \).
Q3: Can this formula be used for any angle A?
A: Yes, the formula works for any angle A where tan(A/3) is defined, except when the denominator equals zero.
Q4: How is this formula derived?
A: The formula is derived from the triple-angle identity for tangent: \( \tan(3\theta) = \frac{3\tan\theta - \tan^3\theta}{1 - 3\tan^2\theta} \), by substituting \( \theta = A/3 \).
Q5: Are there similar formulas for other trigonometric functions?
A: Yes, similar triple-angle formulas exist for sine and cosine functions as well.