(1) Common Formulas / Geometry / Basic Trig

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Last updated 1:07 AM on 9/21/26
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39 Terms

1
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Midpoint formula

(x1+x22,y1+y22)\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

2
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Distance formula between two points

d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

3
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Quadratic Formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2-4ac}}{2a}

4
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Pythagorean Theorem

a2+b2=c2a^2+b^2=c^2

5
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sin⁡(θ)\sin(\theta) definitions

sin⁡(θ)=opphyp=yr=1csc⁡(θ)\sin(\theta) = \frac{\text{opp}}{\text{hyp}} = \frac{y}{r} = \frac{1}{\csc(\theta)}

6
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cos⁡(θ)\cos(\theta) definitions

cos⁡(θ)=adjhyp=xr=1sec⁡(θ)\cos(\theta) = \frac{\text{adj}}{\text{hyp}} = \frac{x}{r} = \frac{1}{\sec(\theta)}

7
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tan⁡(θ)\tan(\theta) definitions

tan⁡(θ)=oppadj=yx=1cot⁡(θ)\tan(\theta) = \frac{\text{opp}}{\text{adj}} = \frac{y}{x} = \frac{1}{\cot(\theta)}

8
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cot⁡(θ)\cot(\theta) definitions

cot⁡(θ)=adjopp=xy=1tan⁡(θ)\cot(\theta) = \frac{\text{adj}}{\text{opp}} = \frac{x}{y} = \frac{1}{\tan(\theta)}

9
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csc⁡(θ)\csc(\theta) definitions

csc⁡(θ)=hypopp=ry=1sin⁡(θ)\csc(\theta) = \frac{\text{hyp}}{\text{opp}} = \frac{r}{y} = \frac{1}{\sin(\theta)}

10
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sec⁡(θ)\sec(\theta) definitions

sec⁡(θ)=hypadj=rx=1cos⁡(θ)\sec(\theta) = \frac{\text{hyp}}{\text{adj}} = \frac{r}{x} = \frac{1}{\cos(\theta)}

11
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Quotient Identity for tan⁡(u)\tan(u)

tan⁡(u)=sin⁡(u)cos⁡(u)\tan(u) = \frac{\sin(u)}{\cos(u)}

12
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Quotient Identity for cot⁡(u)\cot(u)

cot⁡(u)=cos⁡(u)sin⁡(u)\cot(u) = \frac{\cos(u)}{\sin(u)}

13
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Pythagorean Identities

sin⁡2(u)+cos⁡2(u)=1\sin^2(u)+\cos^2(u)=1, 1+tan⁡2(u)=sec⁡2(u)1+\tan^2(u)=\sec^2(u), 1+cot⁡2(u)=csc⁡2(u)1+\cot^2(u)=\csc^2(u)

14
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Area and Circumference of a circle

A=πr2A = \pi r^2 and C=2πrC = 2\pi r

15
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Area of a Parallelogram

A=bhA = bh

16
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Area of a Trapezoid

A=12h(b1+b2)A = \frac{1}{2}h(b_1+b_2)

17
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Area of a Triangle

A=12bhA = \frac{1}{2}bh

18
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30-60-90 Triangle properties

Hypotenuse is 22 times short leg; long leg is 3\sqrt{3} times short leg

19
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45-45-90 Triangle properties

Hypotenuse is 2\sqrt{2} times leg; two legs are equal

20
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sin⁡(θ)\sin(\theta) definitions

sin⁡(θ)=opphyp=yr=1csc⁡(θ)\sin(\theta) = \frac{\text{opp}}{\text{hyp}} = \frac{y}{r} = \frac{1}{\csc(\theta)}

21
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cos⁡(θ)\cos(\theta) definitions

cos⁡(θ)=adjhyp=xr=1sec⁡(θ)\cos(\theta) = \frac{\text{adj}}{\text{hyp}} = \frac{x}{r} = \frac{1}{\sec(\theta)}

22
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tan⁡(θ)\tan(\theta) definitions

tan⁡(θ)=oppadj=yx=1cot⁡(θ)\tan(\theta) = \frac{\text{opp}}{\text{adj}} = \frac{y}{x} = \frac{1}{\cot(\theta)}

23
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cot⁡(θ)\cot(\theta) definitions

cot⁡(θ)=adjopp=xy=1tan⁡(θ)\cot(\theta) = \frac{\text{adj}}{\text{opp}} = \frac{x}{y} = \frac{1}{\tan(\theta)}

24
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csc⁡(θ)\csc(\theta) definitions

csc⁡(θ)=hypopp=ry=1sin⁡(θ)\csc(\theta) = \frac{\text{hyp}}{\text{opp}} = \frac{r}{y} = \frac{1}{\sin(\theta)}

25
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sec⁡(θ)\sec(\theta) definitions

sec⁡(θ)=hypadj=rx=1cos⁡(θ)\sec(\theta) = \frac{\text{hyp}}{\text{adj}} = \frac{r}{x} = \frac{1}{\cos(\theta)}

26
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Quotient Identity for tan⁡(u)\tan(u)

tan⁡(u)=sin⁡(u)cos⁡(u)\tan(u) = \frac{\sin(u)}{\cos(u)}

27
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Quotient Identity for cot⁡(u)\cot(u)

cot⁡(u)=cos⁡(u)sin⁡(u)\cot(u) = \frac{\cos(u)}{\sin(u)}

28
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Pythagorean Identities

sin⁡2(u)+cos⁡2(u)=1\sin^2(u)+\cos^2(u)=1, 1+tan⁡2(u)=sec⁡2(u)1+\tan^2(u)=\sec^2(u), 1+cot⁡2(u)=csc⁡2(u)1+\cot^2(u)=\csc^2(u)

29
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Area and Circumference of a circle

A=πr2A = \pi r^2 and C=2πrC = 2\pi r

30
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Area of a Parallelogram

A=bhA = bh

31
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Area of a Trapezoid

A=12h(b1+b2)A = \frac{1}{2}h(b_1+b_2)

32
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Area of a Triangle

A=12bhA = \frac{1}{2}bh

33
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30-60-90 Triangle properties

Hypotenuse is 22 times short leg; long leg is 3\sqrt{3} times short leg

34
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45-45-90 Triangle properties

Hypotenuse is 2\sqrt{2} times leg; two legs are equal

35
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sin⁡(0∘)\sin(0^\circ)

00

36
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sin⁡(30∘)\sin(30^\circ)

12\frac{1}{2}

37
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sin⁡(45∘)\sin(45^\circ)

22\frac{\sqrt{2}}{2}

38
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sin⁡(60∘)\sin(60^\circ)

32\frac{\sqrt{3}}{2}

39
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sin⁡(90∘)\sin(90^\circ)

11