Precalc Summative 2 Formula Flashcards

cos(a +or- b)

cosacosb +or- sinasinb (The sign flips)

sin(a +or- b)

sinacosb +or- cosasinb (Same sign)

tan(a +or- b)

(tana +or- tanb) / (1 +or- tanatanb) The bottom sign flips, the top stays the same

sin2a

2sinacosa

cos2a

[cos^2a - sin^2a] or [2(cos^2)a - 1] or [1 - 2(sin^2)a]

tan2a

(2tan a) / (1 - tan^2 a)

Converting from polar to cartesian coordinates for x

x = r cos(theta)

Converting from polar to cartesian coordinates for y

y = r sin(theta)

Converting from cartesian to polar coordinates for r

r = sqrt(x²+y²)

Converting from cartesian to polar coordinates for tan(theta)

tan(theta) = y/x

Law of Sines

(sinA)/a = (sinB)/b = (sinC)/c

Law of Cosines

c² = a² + b² - 2ab cos(C)

Component form of a vector

(x2 - x1, y2 - y1)

Parametric Equations

(x,y) = (x0, y0) + t(a,b)

x = x0 + ta

y = y0 + tb

How to calculate perpendicular vectors

Use the dot product

Dot Product

v1 dot v2 = (x1)(x2) + (y1)(y2)

Equation for the angle between two vectors

cos(theta) = (a dot b) / (magnitude of a)(magnitude of b)