Date post: | 19-Feb-2017 |
Category: |
Education |
Upload: | shaun-wilson |
View: | 140 times |
Download: | 0 times |
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