Download - 11X1 T04 03 pythagorean trig identities (2011)

Pythagorean Trig Identities


y

x

1

xy


y

x

2 2 1x y

1

xy


y

x

2 2 1x y

sin1sin

y

y

1

xy


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

1

xy


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

2 2sin cos 1

1

xy


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

2 2sin cos 1

2Divide by sin

1

xy


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

2 2sin cos 1

2Divide by sin 2 2

2 2 2sin cos 1sin sin sin

1

xy


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

2 2sin cos 1

2Divide by sin 2 2


2 21 cot cosec

1

xy


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

2 2sin cos 1

2Divide by sin 2 2


2 21 cot cosec

1

xy

2Divide by cos


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

2 2sin cos 1

2Divide by sin 2 2


2 21 cot cosec

1

xy

2Divide by cos 2 2

2 2 2sin cos 1cos cos cos


y

x

2 2 1x y

sin1sin

y

y

cos1cos

x

x

2 2sin cos 1

2Divide by sin 2 2


2 21 cot cosec

1

xy

2Divide by cos 2 2

2 2 2sin cos 1cos cos cos

2 2tan 1 sec

2 2sin cos 1 2 21 tan sec 2 21 cot cosec


In addition: sin tancos



3e.g. ( ) If cos and tan is negative, find sin4

i




i

3 4




i

3 4

7




i

3 4

7

4th quadrant




i

3 4

7

4th quadrant

7sin4

(ii) Simplify;2) 1 cosa


21 1 sin


21 1 sin 2

2

1 1 sinsin


21 1 sin 2

2

1 1 sinsin

2 2) sec tanb A A


21 1 sin 2

2

1 1 sinsin

2 2) sec tanb A A2 21 tan tanA A

1


21 1 sin 2

2

1 1 sinsin


1

) tan cosc


21 1 sin 2

2

1 1 sinsin


1

) tan cosc sin coscos 1

sin


21 1 sin 2

2

1 1 sinsin


1


sin

22sec 2 tan Prove

4 tan 2iii


21 1 sin 2

2

1 1 sinsin


1


sin

22sec 2 tan Prove

4 tan 2iii

22sec 24 tan


21 1 sin 2

2

1 1 sinsin


1


sin

22sec 2 tan Prove

4 tan 2iii

22sec 24 tan

22 1 tan 2

4 tan


21 1 sin 2

2

1 1 sinsin


1


sin

22sec 2 tan Prove

4 tan 2iii

22sec 24 tan

22 1 tan 2

4 tan

22 2 tan 24 tan


21 1 sin 2

2

1 1 sinsin


1


sin

22sec 2 tan Prove

4 tan 2iii

22sec 24 tan

22 1 tan 2

4 tan

22 2 tan 24 tan

22 tan4 tan


21 1 sin 2

2

1 1 sinsin


1


sin

22sec 2 tan Prove

4 tan 2iii

22sec 24 tan

22 1 tan 2

4 tan

22 2 tan 24 tan

22 tan4 tan

tan2


21 1 sin 2

2

1 1 sinsin


1


sin

22sec 2 tan Prove

4 tan 2iii

22sec 24 tan

22 1 tan 2

4 tan

22 2 tan 24 tan

22 tan4 tan

tan2

when proving trig identitiesyou can;

1. start with LHS and prove RHS2. start with RHS and prove LHS

3. work on LHS and RHS independently and show they

equal the same thing

NEVER SOLVE LIKE AN EQUATION

Exercise 4E; 1a, 2b, 3ac, 4bd, 5, 7, 9*

Exercise 4F; 3a, 4b, 5c, 6ac, 7bd, 8ac, 10ad,11acegi, 12bdfhj, 13ac, 14bd, 15ac,

16acegik, 17*a

Download - 11X1 T04 03 pythagorean trig identities (2011)

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