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1. 9.3: Double-Angle, Half-Angle, and Reduction Formulas
Link: https://math.libretexts.org/Bookshelves/Algebra/Algebra_and_Trigonometry_1e_(OpenStax)/09%3A_Trigonometric_Identities_and_Equations/9.03%3A_Double-Angle_Half-Angle_and_Reduction_Formulas
Description: WebUse the double-angle formula for cosine to write \(\cos(6x)\) in terms of \(cos(3x)\). Solution \[\begin{align*} \cos(6x)&= \cos(3x+3x)\\[4pt] &= \cos 3x \cos 3x-\sin 3x \sin 3x\\[4pt] &= {\cos}^2 3x-{\sin}^2 3x \end{align*}\] Analysis. This example illustrates that we can use the double-angle formula without having exact values.
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2. Double Angle Formulas - What Are Double Angle Formulas?
Link: https://www.cuemath.com/double-angle-formulas/
Description: WebSome important double angle formulas are: sin 2A = 2 sin A cos A; cos 2A = cos 2 A - sin 2 A; tan 2A = (2 tan A) / (1 - tan 2 A) How To Derive Double Angle Formulas? We substitute A = B in the sum formulas of sin, cos, and tan functions to derive the double angle formulas.
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3. Double-Angle Formulas -- from Wolfram MathWorld
Link: https://mathworld.wolfram.com/Double-AngleFormulas.html
Description: Web4 days ago · Formulas expressing trigonometric functions of an angle 2x in terms of functions of an angle x, sin (2x) = 2sinxcosx (1) cos (2x) = cos^2x-sin^2x (2) = 2cos^2x-1 (3) = 1-2sin^2x (4) tan (2x) = (2tanx)/ (1-tan^2x). (5) The corresponding hyperbolic function double-angle formulas are sinh (2x) = 2sinhxcoshx (6) cosh (2x) = 2cosh^2x-1 (7) tanh (2x ...
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4. Trigonometric Equations - Double Angle Formula - Brilliant
Link: https://brilliant.org/wiki/trigonometric-equations-double-angle-formula/
Description: WebThe trigonometric double angle formulas give a relationship between the basic trigonometric functions applied to twice an angle in terms of trigonometric functions of the angle itself. Contents. Double Angle Formulas. Hyperbolic Double Angle Formulas. Examples. Double Angle Formulas. Double angle formulas: We have.
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5. Double Angle Identities | Brilliant Math & Science Wiki
Link: https://brilliant.org/wiki/double-angle-identities/
Description: Web4 days ago · Double Angle Formulas. \begin {aligned} \sin 2x &= 2\sin x\cos x \\\\ \cos 2x &= \cos^2 x - \sin^2 x \\ &= 2\cos^2 x - 1 \\ &= 1 - 2\sin^2 x \\\\ \tan 2x &= \frac {2\tan x} {1 - \tan^2 x} \end {aligned} sin2x cos2x tan2x = 2sinxcosx = cos2 x−sin2 x = 2cos2 x−1 = 1− 2sin2 x = 1−tan2 x2tanx. From these formulas, we also have the following identities:
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6. Double Angle Formula Calculator | Identities
Link: https://www.omnicalculator.com/math/double-angle-formula
Description: WebMay 4, 2023 · There are a few formulas for the cos double angle. The three most popular cosine of a double angle equations are: \cos (2\cdot\theta)=\cos^2 (\theta)-\sin^2 (\theta) cos(2 ⋅ θ) = cos2(θ) − sin2(θ) Which involves both the sine and the cosine: \cos (2\cdot\theta)=2\cdot\cos^2 (\theta)-1 cos(2 ⋅ θ) = 2 ⋅ cos2(θ) − 1.
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7. Double angle formulas: using cosine double-angle identity …
Link: https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/double-angle-formula-for-cosine-example-c
Description: WebThe cosine double angle formula tells us that cos(2θ) is always equal to cos²θ-sin²θ. For example, cos(60) is equal to cos²(30)-sin²(30). We can use this identity to rewrite expressions or solve problems.
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8. 9.3 Double-Angle, Half-Angle, and Reduction Formulas
Link: https://openstax.org/books/algebra-and-trigonometry-2e/pages/9-3-double-angle-half-angle-and-reduction-formulas
Description: WebThe double-angle formulas are a special case of the sum formulas, where α = β. α = β. Deriving the double-angle formula for sine begins with the sum formula, sin ( α + β ) = sin α cos β + cos α sin β sin ( α + β ) = sin α cos β + cos α sin β
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9. 3. Double Angle Formulas - Interactive Mathematics
Link: https://www.intmath.com/analytic-trigonometry/3-double-angle-formulas.php
Description: WebFormulas for the sin and cos of double angles. Exact value examples of simplifying double angle expressions.
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10. 7.4: Double-Angle, Half-Angle, and Reduction Formulas
Link: https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_2e_(OpenStax)/07%3A_Trigonometric_Identities_and_Equations/7.04%3A_Double-Angle_Half-Angle_and_Reduction_Formulas
Description: WebPrecalculus & Trigonometry. Precalculus 2e (OpenStax) 7: Trigonometric Identities and Equations. Expand/collapse global location. 7.4: Double-Angle, Half-Angle, and Reduction Formulas. Page ID. OpenStax. Learning Objectives. In this section, you will: