AP Calculus Review

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23 Terms

1
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dy/dx(sinx)

cosx

2
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dy/dx(cosx)

-sinx

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dy/dx(cscx)

-cscxcotx

4
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dy/dx(secx)

secxtanx

5
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dy/dx(tanx)

sec²x

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dy/dx(cotx)

-csc²x

7
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dy/dx(sin-1x)

1/√1-x²

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dy/dx(cos-1x)

-1/√1-x²

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dy/dx(csc-1x)

-1/IxI√x²-1

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dy/dx(sec-1x)

1/IxI√x²-1

11
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dy/dx(tan-1x)

1/1+x²

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dy/dx(cot-1x)

-1/1+x²

13
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Circles

Area: πr²

Circumference: 2πr

(x-h)²+(y-k)²=r²

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Sectors of a Circle

Area: θr²/2

Arc Length: s=rθ

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Right Triangles

a²+b²=c²

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All Triangles

Area: 1/2bh

Area: 1/2bcsinA

s = a+b+c/2 Area: √s(s-a)(s-b)(s-c)

Equilateral Area: √3/4(s²)

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Law of Sines

sinA/a = sinB/b = sinC/c

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Law of Cosines

a^2=b^2+c^2-2bc\cos A

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Trapezoids

A=\frac{\left(a+b\right)}{2}h

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Spheres

V=\frac43\pi r^3

S=4\pi r^2

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Cones

V=\frac13\pi r^2h

S=\pi r^2+\pi rl

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Cylinders

V=\pi r^2h

S=2\pi rh+2\pi r^2

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Prisms

V=Bh