Kartlar: Formulas, Geometry and Trigonometry, SAT | Quizlet

distance formula

The distance between (x₁, y₁) and (x₂, y₂) is: sqrt[(x₂ − x₁)² + (y₂ − y₁)²]

mid-point formula

The midpoint between (x₁, y₁) and (x₂, y₂) is: ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

area of triangle

Area = 1/2 × base × height

circle area

Area = pi × r², where r is the radius.

length of arc

Arc length = (n / 360) × 2 × pi × r, where n is the central angle in degrees.

area of sector

Area of sector = (n / 360) × pi × r², where n is the central angle in degrees.

rectangle area

Area = length × width

parallelogram area

Area = base × height

rectangular solid volume

Volume = length × width × height

right cylinder volume

Volume = pi × r² × h, where r is the radius and h is the height.

equation of circle

If center is (h, k) and radius r: (x − h)² + (y − k)² = r²

special sin cos relationship

sin²(angle) + cos²(angle) = 1. This fundamental identity shows that the sum of the squares of sine and cosine of any angle is always 1.

trapezoid area

To find the area, add the two bases, divide by 2, and then multiply by the height: area = (base1 + base2) / 2 × height.

How do you find the distance between two points on a coordinate graph?

Use the distance formula: distance = sqrt[(x2 − x1)² + (y2 − y1)²], where (x1, y1) and (x2, y2) are the points.

How do you find the area of a triangle?

The area of a triangle is found using the formula: Area = 1/2 × base × height. The height is the perpendicular distance from the base to the opposite vertex.

What is the Pythagorean Theorem?

In a right triangle: (leg1)² + (leg2)² = (hypotenuse)². For legs of lengths 2 and 3: 2² + 3² = 4 + 9 = 13, so the hypotenuse is the square root of 13.

How do you find the volume of a rectangular solid?

Volume = length × width × height (V = lwh). For a cube, where all sides are equal, volume = edge³ (V = e³).

How do you find the volume of a cylinder?

Volume = pi × r² × h, where r is the radius and h is the height of the cylinder.

reflecting across x axis

(x, -y)

The y-coordinate is multiplied by -1. The x-coordinate remains unchanged.

reflecting across y axis

(-x, y)

The x-coordinate is multiplied by -1. The y-coordinate remains unchanged.

circle equation central-radius form

(x−h)² + (y−k)² = r²

The center is at (h, k) and r is the radius.

area of a triangle

A = 1/2 × base × height. This formula gives the area of a triangle using its base and height.

area of a circle

A = pi × r². This formula gives the area of a circle using its radius (r).

Pythagorean theorem

a² + b² = c²; in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.

Pythagorean theorem

In a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides: a² + b² = c².

formula for the area of a CIRCLE

Area = pi times the square of the radius; A = pi r².

special formula for the area of a triangle

Area = one-half base times height; A = 1/2 b h.

formulas for the area of a parallelogram, rectangle, and a square

Area equals base times height for parallelograms; length times width for rectangles and squares.

formula for the circumference of a circle

C = 2πr, where r is the radius.

formula for the volume of a rectangular solid and a cube

Cube: V = side³. Rectangular solid: V = l × w × h.

formula for the volume of a PYRAMID or CONE

V = 1/3 × B × h, where B is the base area and h is the height.

midpoint formula

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

equation of a circle

(x − h)² + (y − k)² = r²; where (h, k) is the center and r is the radius.

Pythagorean theorem

a² + b² = c², where a and b are legs and c is the hypotenuse of a right triangle.

formula for the area of a CIRCLE

A = pi r², where r is the radius.

special formula for the area of a triangle

Area = 1/2 base times height (1/2 bh).

formula for the volume of a PYRAMID or CONE

Volume = 1/3 x base area x height (V = 1/3 Bh).

midpoint formula

Midpoint: ((x1 + x2) / 2, (y1 + y2) / 2).

equation of a circle

(x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.

Pythagorean Theorem

In a right triangle: a² + b² = c², where c is the hypotenuse. Use this formula to find a missing side.

Area of a Circle

A = πr², where r is the radius. Multiply pi by the radius squared to find the area.

Circumference of a Circle

C = 2πr or C = πd, where r is the radius and d is the diameter of the circle.

Area of a Sector (Circle)

Area = (n/360) × πr², where n is the central angle in degrees and r is the radius.

Arc Length of a Sector (Circle)

Arc length = (n/360) × 2πr, where n is the central angle in degrees and r is the radius.

Area of a Polygon

A = (1/2)aP, where a is the apothem (distance from center to midpoint of a side) and P is the perimeter.

Area of a Trapezoid

A = 1/2 × height × (base1 + base2).

Surface Area of a Sphere

SA = 4 × pi × r squared. Multiply 4 by pi and by the radius squared.

Surface Area of a Prism

SA = 2lw + 2lh + 2wh or SA = 2B + Ph, where B is base area, P is base perimeter, h is height.

Right triangle side lengths

Use the Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse of a right triangle.

Surface Area of a box (also called right rectangular prism)

Surface area is the sum of all outer surfaces: 2lw + 2wh + 2lh, where l is length, w is width, and h is height. It is not the same as volume.

coordinate geometry:

equation of a circle

The equation is (x − h)² + (y − k)² = r², where (h, k) is the center and r is the radius.

sin

Ratio of the opposite side to the hypotenuse in a right triangle.

cos

Ratio of the adjacent side to the hypotenuse in a right triangle.

tan

Ratio of the opposite side to the adjacent side in a right triangle.

Pythagorean Theorem

a² + b² = c², relating the sides of a right triangle.

Midpoint Formula

The midpoint of (x1, y1) and (x2, y2) is ((x1 + x2) / 2, (y1 + y2) / 2).

distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

formulas for the area of a parallelogram, rectangle, and a square

length x width

formula for the volume of a rectangular solid and a cube

Cube: V=side³ Rectangular solid: l*w*h

distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Area of a Triangle

A=½(Base)(Height)

A=½bh

Area of a Square

A=(side)(side)

A=s²

Diagonal of a Square

Diagonal=side(√2)

D=s√2

Area of a Rectangle

A=(length)(width)

A=lw

Perimeter of a Rectangle

P=2(length)+2(width)

P=2l+2w

Area of a Parallelogram

A=(base)(height) or A=bh

Surface Area of a Cylinder

SA=2πr²+2πrh

Volume of a Sphere

V=(4/3)πr³

Volume of a Cube

V=side³

V=s³

Volume of a Cylinder

V=πr²h

Volume of a Prism

V=lwh

trigonometry:

sin(angle) =

ratio of sides:

sin(angle) = opposite / hypotenuse

Remember: SOH CAH TOA

Trig functions take angles as input and give side ratios as output.

sin, cos, and tan are abbreviations of sine, cosine, and tangent, respectively.

trigonometry:

SOH CAH TOA

sin(angle) = opposite / hypotenuse

cos(angle) = adjacent / hypotenuse

tan(angle) = opposite / adjacent

trigonometry:

cos(angle) =

ratio of sides:

cos(angle) = adjacent / hypotenuse

Remember: SOH CAH TOA

Trig functions take angles as input and give side ratios as output.

sin, cos, and tan are abbreviations of sine, cosine, and tangent, respectively.

trigonometry:

tan(angle) =

ratio of sides:

tan(angle) = opposite / adjacent

Remember: SOH CAH TOA

Trig functions take angles as input and give side ratios as output.

sin, cos, and tan are abbreviations of sine, cosine, and tangent, respectively.