Law of Sines

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SinA / a = SinB / b = SinC / c

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40 Terms

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Law of Cosines

a² = b² + c² - 2bc * cosA

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Set of all points where z = 0 is called….

The xy - plane

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Set of all points where x = 0 is called…

The zy - plane

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Set of all points where y = 0 is called…

The xz - plane

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Coordinate Planes

The xy, yz, and xz planes

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Distance Formula

dis(P, Q) = √(x1 - x2)² + (y1 - y2) + (z1 - z2)

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Midpoint Formula

Take the average of each coordinate:

p + q / 2

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Polar Coordinates

(r,θ)

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θ (for polar)

Distance off of the positive x-axis

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r (radius) in polar

Distance from the origin

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Cartesian/Rectangular Coordinates

(x,y,z)

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Converting Polar and Cartesian

x = rcosθ

y = rsinθ

r² = x² = y²

θ = tan-1(y/x)

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Cylindrical Coordinates

(r, θ, z)

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r in Cylindrical Coordinate

Distance to the z- axis

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Spherical Coordinates

(P, θ, Φ)

(Rho, Theta, Phi)

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P (Rho)

(sph) Distance to the origin

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θ

(Same as cylindrical) angle off of the positive x-axis in xy-plane

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Φ (Phi)

tilt angle off of the positive z-axis

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Sphere Equation (centered at origin) in cartesian

x² + y² + z² = p²

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Sphere Equation (centered at origin) in cylindrical

r² + z² = p²

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Sphere Equation (centered at origin) in spherical

p = a

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Circle equation (centered at origin) in cartesian

x² + y² = r²

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Circle equation (centered at origin) in polar

r = a

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The length of one wavelet is…

The period

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Amplitude

The maximum height the curve reaches

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Formula for Period

2π/b

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Standard Form of Sinusoidal Curves

y = asin(bx)

y = acos(bx)

*(a = amplitude)

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y = af(x)

a > 1 means…

Vertical Stretch

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y = af(x)

0 < a < 1 means…

Vertical Shrink

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y = f(bx)

b > 1 means…

(big #)

Horiztonal Shrink

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y = f(bx)

0 < b < 1 means….

(small #)

Horizontal Stretch

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Parabola

The set of all points that are equidistant from the focus point and the directrix line

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Standard Form of a Parabola

±4c(y-k) = (x-h)²

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c means…

(parabola)

distance from the vertex to the focus/directrix

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The vertex comes from…

(h,k)

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h tells us…

(parabola)

The x-value of focus and vertex and the AOS

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± tells us ….

(parabola equation)

(-) = parabola opens down

(+) = parabola opens up

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Ellipse

The set of all points where the sum of distances between foci is constant

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Standard Form of an Ellipse:

(x-h)²/a² + (y-k)²/b² = 1

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