trigonometry

For dummies

by Norma

Trigonometry topics discussed

Unit circle Quadrants Sine cosine tangent Secant cosecant cotangent Types of angles (initial terminal conterminal

reference) Radian and degree measure Pythagorean theorem Trig identities

What is trigonometry What is trigonometry

Trigonometry is the study of triangles and Trigonometry is the study of triangles and anglesangles

Sine cosine tangentSine cosine tangentwhat are they?what are they?

Sine cosine and tangent is used when dealing with right triangles

A way to remember sine cosine and tangent is SohCahToa

Unit circle

The unit circle is used when dealing with sine cosine and tangent\

The radius of the unit circle is 1

The coordinates of the circle are (x,y) or (sin, cos)

quadrantquadrant

A quadrant is a quarter of a A quadrant is a quarter of a planeplane. The . The x-axisx-axis and and y-axisy-axis divide the x-y plane into divide the x-y plane into four quadrants. four quadrants.

Sine, cosine and tangent measures Sine, cosine and tangent measures on the unit circleon the unit circle

Angle values for trigAngle values for trig

Initial and terminal angles Initial and terminal angles reference anglereference angle

AN ANGLEAN ANGLE is in standard position when its is in standard position when its vertexvertex A is at the origin of the A is at the origin of the x-yx-y plane, plane, and its Initial side AB lies along the positive and its Initial side AB lies along the positive xx-axis, while its Terminal side AC has -axis, while its Terminal side AC has rotated. rotated.

The reference angle is defined as the acute The reference angle is defined as the acute angle between the terminal side of the angle between the terminal side of the given angle and the x axis. The given angle given angle and the x axis. The given angle may be in degrees or radians. may be in degrees or radians.

The reference angle is defined as

Convert degrees to radians

          to convert radians to degrees, multiply by 180/, like this:

                                                                                                    

to convert degrees to radians, multiply by , like this:

                                                                                          

What are reciprocal trigonometric functions?

Reciprocal of trigonometric functions are the opposite of sine cosine and tangent functions

Reciprocal of sine is 1 over sine or csc Reciprocal of cosine is 1 over cosine or sec Reciprocal of tangent is 1 over tangent or sin

over cos or cot

Pythagorean identities

Pythagorean identities a)sin²θ + cos²θ  =  1 b)1 + tan²θ  =  sec²θ c)1

+ cot²θ  =  csc ²θa')     sin²θ  =  1 − cos²θ. b) cos²θ  =  1 − sin²θ.

Trig for dummiesTrig for dummies