Double Angle and Half Angle Formulas

Recovering the Double Angle Formulas

Using the sum formula and difference formulas for Sine and Cosine we can observe the following identities:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \sin(2\theta )=2\sin(\theta )\cos(\theta )}

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \cos(2\theta )=\cos ^{2}(\theta )-\sin ^{2}(\theta )}

Using the Pythagorean Identities for trigonometric functions we can also see that:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(2\theta) = 1 - 2\sin^2(\theta)}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(2\theta) = 2\cos^2(\theta) - 1}

Half Angle Formulas

Using the last two double angle formulas we can now solve for the half angle formulas:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin(\theta) = \sqrt{\frac{1 - \cos(2\theta)}{2}}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\theta) = \sqrt{\frac{1 + \cos(2\theta)}{2}}}

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