JLSS Trigonometry

c² = a² + b²

Pythagorean theorem

SOH CAH TOA

Trigonometric functions

CHO SHA CAO

Inverse trigonometric function

Angle

Formed from two rays that have the same endpoint

Segment

Line with two endpoints

Ray

Line with one endpoint

90

Angle of a right triangle

less than 90 deg

Acute angle

More than 90 deg

Obtuse

CCW

Movement of an angle (positive)

Rad = S/r

Formula for radian, given arc and radius.

2pi r

Circumference of a circle

180/pi

Formula for rad-deg conversion

Coterminals

Different angles that end up on the same terminal side.

+-360 (depending on the sign)

How to solve to coterminals?

(sqr3/2, 1/2)

x and y values of 30deg

(sqr2/2, sqr2/2)

x and y values of 45deg

(1/2, sqr3/2)

x and y values of 60deg

-80 or -360

How to get reference angle?

csc

1/sinθ

sec

1/cosθ

cot

1/tanθ

S = θr

Formula for the arc length

A = 1/2θr²

Formula for area of sector

v = s/t

Formula for linear speed

w = θ/t

Formula for angular speed

v = rw

Formula for linear and angular

cos(x)

cos(-x)

-sin(x)

sin(-x)

1

sin² + cos² =

sec²

1 + tan² =

csc²

1 + cot² =

bw

Area of rectangle

1/2bh

Area of triangle

sqr3/4s²

Area of equilateral triangle

s²

Area of square

pi r²

Area of circle

As = A1 - A2

Area of shaded region

sinθ

cos(90-θ)

tanθ

cot(90-θ)

cscθ

sec(90-θ)