Unformatted text preview: Twoangle 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 doubleangles 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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 Spring '15
 B.Frye
 Calculus, PreCalculus, Angles, Formulas

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