Two Angles Formulas

# Two Angles Formulas - Two-angle Formulas and Other Related...

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Unformatted text preview: Two-angle Formulas and Other Related Formulas In the applications of trigonometry, a set of formulas involving two angles or real numbers, or multiples of a single angle or real number is often required. Listed below are formulas for addition, subtraction and double-angles for sine, cosine, and tangent. Formulas: 1.cos(u—v)=cosucosv+sinusinv 2. cos (u + v) =cos 11 cos v — sin 11 sin v 3. sin (u+v)=sinucosv+cosusinv 4. sin (u—v)=sinucosv—cosusinv tan u + tan v 5. tan (u + v) = l — tan u tanv tan u — tan v 6. tan (u — V) = 1 + tan u tanv Double angle formulas . . 2 sm 2u = 2 sm u cos u cos 2n = cos To summarize in words: (1) The cosine of the difference of two angles equals the cosine of the ﬁrst times the cosine of the second plus the sine of the ﬁrst times the sine of the second. (2) The cosine of the sum of two angles equals the cosine of the ﬁrst times the cosine of the second minus the sine of the ﬁrst times the sine of the second. (3) The sine of the sum of two angles equals the sine of the ﬁrst times the cosine of the second plus the cosine of the ﬁrst times the sine of the second. (4) The sine of the diﬂerence of two angles equals the sine of the ﬁrst times the cosine of the second minus the cosine of the ﬁrst times the sine of the second. (5) The tangent of the sum of two angles is equal to a fraction whose numerator is the tangent of the ﬁrst plus the tangent of the second, and whose denominator is 1 minus the product of their tangents. (6) The tangent of the difference of two angles is equal to a fraction Whose numerator is the tangent of the ﬁrst minus the tangent of the second, and Whose denominator is 1 plus the product of their tangents. 2tanu . 2 u—sm u tan2u= l—tan u 2 cos 2n = 2cos u — 1 cos2u=1—-28in2u ...
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