pre-calc final semester 2 (ch 5-7)

-sin x

sin (-x)

-csc x

csc (-x)

cos x

cos (-x)

sec x

sec (-x)

-tan x

tan (-x)

-cot x

cot (-x)

sin x / cos x

tan x =

cos x

sin (pi/2 - x) =

cot x

tan (pi/2 - x)

csc x

sec (pi/2 - x)

sin²x + cos²x = 1

pythagorean identity

2sinxcosx

sin 2x =

cos²x - sin²x

2cos²x - 1

1 - 2sin²x

cos2x =

2tanx/ 1 - tan²x

tan 2x =

a/sin A = b/sin B = c/sin C

law of sines

no triangle

a is acute, a < h, ass case

two triangles

a is acute, h < a < b, ass case

no triangle

a is obtuse, a< b, ass case

A = ½ (base) (height)

A = ½ bc(sinA)

area of a triangle

a² = b² + c² - 2bc (cos A)

b² = a² + c² - 2ac (cos B)

c² = a² + b² - 2ab (cos C)

law of cosines

√s(s-a)(s-b)(s-c)

Heron’s Area Formula

a+b+c/2

s formula

(x2 - x1, y2- y1)

component form of a vector

√v1² + v2²

maginute of a vector

1/magnitude v (v)

unit vector

perpendicular

orthogonal