Relazione fondamentale: sin2 x+ cos2 x= 1 jsinxj= p 1 cos2 x, jcosxj= p 1 sin2 x jsinxj= tanx p 1 + tan2 x, jcosxj= 1 p 1 + tan2 x. Formule di addizione Formule di prostaferesi sin(x+ y) = sinxcosy+ cosxsiny sinx+ siny= 2sin x+ y 2 cos x y 2 sin(x y) = sinxcosy cosxsiny sinx siny= 2sin x y 2 cos x+ y 2 cos(x+ y) = cosxcosy sinxsiny cosx+ cosy

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=⇒ cos(x− y) = cosxcosy + sinxsiny which is the fourth addition formula. Replacing y by −y gives cos(x+ y) = cosxcos(−y)+ sinxsin(−y) = cosxcosy − sinxsiny which is the third addition formula. Now, replacing x by π 2 − x gives cos π 2 −x+ y = cos π 2 −x cosy − sin π 2 −x siny Recalling that sin π 2 −z = cosz and cos

COS Y Uz + Uy = -xu. XER u(x,0) = 2. |g € R. (0, 3) = 2. * = cosy, j=1 y=t+ci,. X = sin(t +ci) + C2. X. = C1, C2 sin y + c. (x, y) = (C,0).

Sin x cos y

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Fourier Transform. • Suppose x(t) and X(f)  a log Fj 2au sin x 2i cot x — ( i + j ) 1 + q ? — 20 ( u cos x + v cos y ) = 0 ( 18 ) дх a log Fij 2av sin y = 2j cot y- ( i + j ) 1 + a2 — 2a ( u cos x + v cosy ) = 0 ( 19 ) ду a  COSI cos 27. , = cos ( c + Y ) , 2 cosa , cosing = COS X + COS Y cos 21.

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Input Target Result. Bits error versus  1 + cos x.

Consider y = -3cos(2πx + 4π). Rewrite as -3cos(2π[x. +2]). • Amplitude = 3. • Curve is flipped over the x-axis. • Period is 2π/b = 2π/2π = 1.

Sin x cos y

(x+cosy)−z⋅siny. Error. Input Target Result. Bits error versus  1 + cos x.

Sin x cos y

hyadan sin x COS Z cos C tang a cos Ctang b cos C.tang b tang x = , tang y  2(sin(x+y)+sin(x−y)) sin(x)sin(y) = 1. 2(cos(x−y)−cos(x+y)) cos(x)cos(y) = 1. 2(cos(x+y)+cos(x−y)). Fourier Transform. • Suppose x(t) and X(f)  a log Fj 2au sin x 2i cot x — ( i + j ) 1 + q ?
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Sin x cos y

−y dx ⇒ dy dx. = ex. −y ey. x. (b) x=sin y ⇒ dx=cos y dy ⇒ dy Evaluate the volume of the body generated by rotating y=sin x ,0 x   Funktionerna y = sin x och y = cos x är alltså definierade för alla x, medan för y = tan x och y = cot x vissa värden måste uteslutas.

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cos (x -y) = cosx ·cosy + sinx ·siny. sin (x +y) = sinx ·cosy sin x ± sin y = 2 cos (x ±y/2)· cos (x-+y/2). cos x ± cosy = -2 sin (x±y/2)· sin (x-+y/2). 1 + cos 2x = 2 cos2 

Share. Save. 112 / 3. Daniel −11−cos(x). Explanation: We have: y=sin(x)1−cos(x). This function can be differentiated using the "quotient rule":. {\displaystyle {\begin{aligned}\sin(-x)&=-\sin(x)&\sin \left({\cfrac {\pi }{2}}-x\right)&=\cos(x)&\sin \left(\pi -x\right)&=+\sin(x)\\\cos(-x)&=+\cos(x)&\cos \left({\cfrac {\pi }{  Om man har en graf, till en funktion f(x) = a sinx + b cosx som går genom punkterna (0(grader), 2), och (60(grader), 0).