THE FUNDAMENTAL TRIGONOMETRIC IDENTITIES

Dr. Shildneck

Spring 2015

THE RECIPROCAL IDENTITIES

THE QUOTIENT IDENTITIES

PYTHAGOREAN IDENTITIES

2 2sin cos 1x x THE BIG ONE!!

PYTHAGOREAN IDENTITIES

2 2sin cos 1x x 2sin x 2sin x 2sin x

1 2cot x 2csc x

PYTHAGOREAN IDENTITIES

2 2sin cos 1x x 2cos x 2cos x 2cos x2tan x 1 2sec x

THE CO-FUNCTION IDENTITIES

In general, anytime you see or , think “co-” function…2 90

THE EVEN/ODD-FUNCTION IDENTITIES

In general, for odd functions, pull the negative out front. for even functions, drop the negative.

ODD

ODD

EVEN

Note: Reciprocal functions have the same sign.

POS

POS

POS

POS

NEG

NEG

NEG

NEG

POS

NEG

POS

NEG

USING IDENTITIES TO EVALUATE TRIG VALUES

Today we will work with Identities to determine the values of trig functions given certain information.

Process1. Determine which Quadrant the terminal side is in.2. Write down all 6 trig functions =3. Fill in what you know.4. Use the appropriate identities (and Pythagorean

Theorem) to determine the remaining trig values.

EX 1.

EX 2.

EX 3

EX 4

EX 5

EX 6

EX 7

EX 8

EX 9

Rewrite the expression so that it is NOT in fractional form:

11 sinx

EX 10

If ,tan 1.52 EX 11

find the value of cot .2

ASSIGNMENTPage 317-318 #1-54 (m3), omit 48