sin2A = 2sinAcosA - St Francis Preparatory School
sin2A = 2sinAcosA cos2A = cos2A ‐ sin2A = 1 ‐ 2sin2A = 2cos2A ‐ 1 tan2A = 2tanA 1 tan2A Equations with Double Angles Example: 1 Find all solutions of x, in the interval 0
Sin2A=2SinA•CosA
Sin2A=2SinA•CosA Cos2A = Cos2A-Sin2A=2Cos2A-1=1-2sin2A 三倍角公式 sin3A = 3sinA-4(sinA)3 cos3A = 4(cosA)3-3cosA tan3a = tana·tan(3 S +a)·tan(3 S-a) 半角公式 sin(2 A)= 2 1 cosA cos( )= 2 1 cosA tan( )= A A 1 cos 1 cos cot( )= A A 1 s 1 s tan( )= A A sin 1 cos = A A 1 s n 和差化积 sina+sinb=2sin 2 a b cos 2 a b
Formulas from Trigonometry
sin2A= 2sinAcosA cos2A= cos2 A sin2 A tan2A= 2tanA 1 2tan A sin A 2 = q 1 cosA 2 cos A 2 = q 1+cos A 2 tan 2 = sinA 1+cosA sin2 A= 1 2 21 2 cos2A cos A= 1 2 + 1 2
Trigonometric Identities Revision : 1
sin2A = 2sinAcosA, (12) cos2A = cos2 A−sin2 A (13) 2 6 Identities for sine squared and cosine squared If we have A = B in equation (10) then we find cosAcosB = 1 2
The double angle formulae - University of Sheffield
3 The formula cos2A = cos2A−sin2A Wenowexaminethisformulamoreclosely Weknowfromanimportanttrigonometricidentitythat cos2 A+sin2 A =1 sothatbyrearrangement sin2 A
Trigonometric function identities
1 + sin2A = cotA 1 cotA+ 1 15 cos + sin cosA sinA = 1 + sin2A cos2A 16 cot cot = sin( ) sin sin 17 tan csc cos = 1 18 cos2 = cot2 1 + cot2 19 1 sinA 1 + sinA = (secA tanA)2 20 (tanA cotA)2 + 4 = sec2 A+ csc2 A 21 cosBcos(A+ B) + sinBsin(A+ B) = cosA 22 tanA sinA secA = sin3 A 1 + cosA 23 2tan2 A 1 + tan2 A = 1 cos2A 24
Exercise 61: Trigonometric Identities - KopyKitab
Sin2A + cos2A = 1 sec2A - tan2A = 1 So, si n A2+ 11 +tan2A =si n A2+1 sec2A sin A 2 + , }, , = sin A 2 H-----=sinA2+(isecA)2 1+tan2A sec2 A v 7 = sin A 2 + (-^ j)2 =sinA2+cos2A= s in A 2 + cos2 A = 1 Q11: V1-cosoi +cos0 =cosec0-cot0 y = cosecQ - cotO A11: We know, sin20+cos20=1 s in 2 9 + cos2 8 = 1
Senior Math Circles: Geometry III
3 (a) Prove that sin2A= 2tanA 1 + tan2 A, where 0
Trigonometric Identities - University of Liverpool
Trigonometric Identities Pythagoras’s theorem sin2 + cos2 = 1 (1) 1 + cot2 = cosec2 (2) tan2 + 1 = sec2 (3) Note that (2) = (1)=sin 2 and (3) = (1)=cos Compound-angle formulae
Table of Integrals
Integrals with Trigonometric Functions Z sinaxdx= 1 a cosax (63) Z sin2 axdx= x 2 sin2ax 4a (64) Z sinn axdx= 1 a cosax 2F 1 1 2; 1 n 2; 3 2;cos2 ax (65) Z sin3 axdx= 3cosax 4a + cos3ax 12a (66) Z cosaxdx=
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