Algebra Trig Formula

Area of a Triangle

Area = 1/2 a b sin(C)
Area= 1/2 c b sin(A)
Area = ½ a c sin(B)

Area of a parallelogram

A = ab sin(θ)

Law of cosines

c² = a² + b² – 2ab cos(C)

Law of cosines (solving for angle)

cos(C) = (a² + b² - c²) / (2ab)

Law of Sines

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

Refrence angle quadrant 1

θ

Refrence angle quadrant 2

180-θ

reference angle quadrant 3

θ-180

reference angle quadrant 4

360-θ

Trig restriction Sine-

[−π/2, π/2]. [-90, 90]

Trig restriction cosine-

[0,π] [0, 180]

Trig restriction tan-

(-π/2, π/2). (-90, 90)

Trig Values – π/3

60°

sin(π/3) =

√3/2

cos(π/3)=

1/2

tan(π/3)

√3

Trig Values – π/4

45°

sin(π/4) =

√2/2

cos(π/4)

√2/2

tan(π/4) =

1

Trig Values – π/6

30°

sin(π/6) =

1/2

cos(π/6) =

√3/2

tan(π/6) =

√3/3

when can you use a²+b²=c²

With a right triangle

The Pythagorean theorem applies in a right triangle to relate the lengths of the legs and the hypotenuse. This relation holds true only when one of the angles is 90 degrees.