Calculate sine, cosine, and tangent for double angles using trigonometric identities.
Last updated: March 2026 | By ForgeCalc Engineering
Double angle formulas are trigonometric identities that express functions of twice an angle (2theta) in terms of functions of the original angle (theta). They are derived from the sum formulas for sine, cosine, and tangent.
These formulas are essential in calculus for simplifying integrals, in physics for analyzing wave interference, and in engineering for signal processing.
cos(2theta) = cos^2(theta) - sin^2(theta)
= 2cos^2(theta) - 1
= 1 - 2sin^2(theta)
Find sin(60 deg) using the double angle formula with theta = 30 deg:
1. Identify: theta = 30 deg, sin(30 deg) = 0.5, cos(30 deg) about 0.866
2. Apply: sin(2 * 30 deg) = 2 * sin(30 deg) * cos(30 deg)
3. Calculate: 2 * 0.5 * 0.866 = 0.866
Final Answer: sin(60 deg) about 0.866
They are all derived from the Pythagorean identity sin^2(theta) + cos^2(theta) = 1. Depending on whether you know sin(theta), cos(theta), or both, one version may be easier to use.
It is undefined when 1 - tan^2(theta) = 0, which happens when theta = 45 deg, 135 deg, etc. (or when theta = pi/4 + n*pi/2 in radians).
Yes, by applying the sum formulas again. For example, sin(3theta) = sin(2theta + theta).
Yes, they are identities, meaning they are true for all values of theta where the functions are defined.
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