Block 2

Trig Relationships

What is to be learned?

• How to use related angles to come up with some pretty interesting rules (not!)

Related Angles Reminder

a0180 – a

180 + a 360 – a

iii

iii iv

Easiest when starting

in Quadrant 1

(Acute angle)

Relations of 700 i 700

ii 180 – 70 = 1100

iii 180 + 70 = 2500

iv 360 – 70 = 2900

Related Angles Reminder

a0180 – a

180 + a 360 – a

iii

iii iv

AS

T C

sin 500 = sin 1300

sin 200 = sin 1600

Rule

sin a0 = sin (180 – a)0

Related Angles Reminder

a0180 – a

180 + a 360 – a

iii

iii iv

AS

T C

cos 500 = cos 1300

cos 200 = cos 1600

Rule

cos a0 = cos (180 – a)0

--

-

Remember

Angles measured anti clockwise from horizontal

a0

Angles measured clockwise from horizontal

-a0

-a0 = 360 – a

and there’s more

Related Angles With Negatives

a0180 – a

180 + a 360 – a

iii

iii iv

AS

T C

sin -300 = sin 3300

= sin 300

Rule

sin a0 = sin (-a)0

-

-

Related Angles With Negatives

a0180 – a

180 + a 360 – a

iii

iii iv

AS

T C

cos -400 = cos 3200

= cos 400

Rule

cos a0 = cos (-a)0

0000 30 3000 454500 60 6000 90 9000

sin

cos

tan

0 π/2π/3

π/4π/6

degrees

rads

0 1½ 1/√2 √3/2

1 √3/21/√2 ½ 0

0 1/√3 1 √3 ∞

Remember These?

0000 30 3000 454500 60 6000 90 9000

sin

cos

tan

0 π/2π/3

π/4π/6

degrees

rads

0 1½ 1/√2 √3/2

1 √3/21/√2 ½ 0

0 1/√3 1 √3 ∞

And Finally

Rule

sin a0 = cos (90 – a)0

Hang on in there…

Some Exciting Trig Rules

sin a0 = sin (180 – a)0

cos a0 = cos (180 – a)0-e.g. if sin 400 = 0.6 then sin 1400 = 0.6

if cos 400 = 0.8 then cos1400 = 0.8

sin a0 = sin (- a)0

cos a0 = cos (- a)0-

e.g. if sin 200 = 0.3 then sin (-20)0 = 0.3e.g. if cos 200 = 0.9 then cos(-20)0 = 0.9

-

-

sin a0 = cos (90 – a)0

e.g. if sin 100 = 0.2 then cos 800 = 0.2

cos a0 = sin (90 – a)0

Key Question

Simplify cos(π/2 – θ) + sin(-θ)

= sin θ – sin θ= 0