# Calculusi Notes

**Pages:**3 (411 words)

**Published:**June 23, 2013

opp.

opp.

hyp.

hyp.

θ

θ

adj.

adj.

tanθ = sinθcosθ = opp.adj.

secθ = 1cosθ = hyp.adj.

cscθ = 1sinθ = hyp.opp.

cotθ = 1tanθ = cosθsinθ = adj.opp.

sin2θ + cos2θ = 1 sin2θ = 1 - cos2θ cos2θ = 1 - sin2θ tan2θ = sec2θ - 1 csc2θ = 1 + cot2θ sec2θ = 1 + tan2θ cot2θ = csc2θ - 1 S

S

A

A

- θ = 360 – θ

T

T

C

C

∴ sin(-θ) = - sinθ & csc(-θ) = - cosecθ

cos(-θ) = + cosθ & sec(-θ) = + secθ

tan(-θ) = - tanθ & cot(-θ) = - cotθ

sinπ2-x=cosx cosπ2-x=sinx tanπ2-x=cotx

cscπ2-x=secx secπ2-x=cscx cotπ2-x=tanx

sin(A±B) = sinAcosB ± cosAsinB

cos(A±B) = cosAcosB ∓ sinAsinB

tan(A±B)= tanA ± tanB1 ∓tanAtanB

∴ sin(2A) = 2sinAcosA

cos(2A) = cos2A – sin2A = 1 – 2sin2A = 2cos2A – 1

tan(2A) = 2tanA1- tan2A

sin2A = 12 - 12cos2A

cos2A = 12 + 12cos2A

tan2A = 1-cos(2A)1+cos(2A)

sinAsinB = 12 ( cos(A-B) – cos(A+B) )

cosAcosB = 12 ( cos(A-B) + cos(A+B) )

sinAcosB = 12 ( sin(A+B) + sin(A-B) )

cosAsinB = 12 ( sin(A+B) – sin(A-B) )

* ddxc=zero

* ddxcx=c

* ddxcy=cdydx

* ddxf(x)±g(x)=d(fx)dx±d(gx)dx

* ddxfx.g(x)=dfxdx.gx+dgxdx.f(x)

* ddxf(x)±g(x)=d(fx)dx±d(gx)dx

* ddxfx.gx.hx=

dfxdx.gx.hx+dgxdx.fx.hx+dhxdx.fx.g(x)

* ddxf(x)g(x)=dfxdx.gx-dgxdx.f(x)[gx]2

* dydx=dydu.dudv.dvdx , where y=fu, u=gv, v=h(x)

* ddxxn=n.xn-1

* ddxyn=n.yn-1.dydx ,where y=f(x)

* dydx=1dxdy

* ddxsinx=cosx

* ddxcscx=-cscx.cotx

* ddxcosx=-sinx

* ddxsecx=secx.tanx

* ddxtanx=sec2x

* ddxcotx=-csc2x

* xn dx=xn+1n+1+c, where n≠-1

* x-1 dx=lnx+c

* (ax+b)n dx= 1a(ax+b)n adx= 1a×(ax+b)n+1n+1+c

* sinx dx= -cosx+c

* cosx dx= sinx+c

* cosec2x dx= -cotx+c

* sec2x dx=...

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