1. Angles between 0 and 360 degrees
IB Studies

2. Investigating angles sin a = sin ___ tan a = tan ___ cos a = cos ___
Ensure that your calculator is in degree mode and write down each of the following to 3 significant figures.
Write down the answers which are the same in pairs:
E.g.
sin 30=sin 150
sin 30
sin 100
tan 30
Can you find a rule based on your findings:
cos 30
sin 80
tan 70
cos 280
tan 210
cos 330
sin a = sin ___
cos 60
sin 50
tan 185
tan a = tan ___
sin 130
tan 250
cos 300
tan 5
sin 150
cos 80
cos a = cos ___

3. Investigating angles - answers
sin 30=sin 150
The Rules:
sin 50=sin 130
sin 80=sin 100
sin a = sin (180-a)
tan 30=tan 210
tan a = tan (180+a)
tan 70=tan 250
tan 5=tan 185
cos a = cos (360-a)
cos 30=cos 330
cos 60=cos 300
cos 80=cos 280

4. Investigating angles - negative answers
Write down the answers which are the same in pairs:
Ensure that your calculator is in degree mode and write down each of the following to 3 significant figures.
E.g.
sin 210=sin 330
Can you find a rule based on your findings, this is a bit harder.
sin 210
sin 200
tan 150
cos 210
sin 315
tan 100
cos 120
tan 330
cos 150
sin (180+a) = sin ___
cos 170
sin 225
tan 280
tan (180-a) = tan ___
sin 340
tan 175
cos 240
tan 355
sin 330
cos 190
cos (180-a) = cos ___

5. Investigating angles - negative answers
The Rules:
sin 210=sin 330
sin 200=sin 340
sin (180+a) = sin (360-a)
sin 225=sin 315
tan 150=tan 330
tan (180-a) = tan (360-a)
tan 100=tan 280
tan 175=tan 355
cos 150=cos 210
cos (180-a) = cos (180+a)
cos 120=cos 240
cos 170=cos 190

6. Why? - The sine graph
2 answers 30o and 150o
2 answers 210o and 330o

7. Why? - The cosine graph
2 answers 60o and 300o
2 answers 120o and 240o

8. Why? - The tangent graph 2 answers 45o and 225o

9. CAST 90o All Sin+ Cos+ Tan+ Sin Sin+ Cos- Tan- 90o to 180o 0o to 90o
The CAST diagram
90o
All
Sin+
Cos+
Tan+
Sin
Sin+
Cos-
Tan-
90o to 180o
0o to 90o 0o
360o
180o
Tan
Sin-
Cos-
Tan+
Cos
Sin-
Cos+
Tan-
270o to 360o
180o to 270o
270o
CAST

10. Answering questions 1 - positives
Just remember the different rules that apply for tan and cos.

11. Answering questions 2 - negatives

12. Questions a) sin40=sin a a) sina=0.906 a=65,115 a=140 b) tan120=tan b
1. Find the values of the letters in the following.
All the letters are between 0 and 360.
2. Find 2 values for the letters in each of the following.
All the letters are between 0 and 360.
a) sin40=sin a
a) sina=0.906
a=65,115
a=140
b) tan120=tan b
b) cosb=-0.819
b=145,225
b=300
c) cos52=cos c
c) tanc=1.43
c=55,235
c=308
d) tan25=sin d
d=205
d) cosd=0.423
d=65,295
e) sin203=sin e
e=337
e) tane=-0.364
e=200,340
f) cos230=cos f
f=130
f) sinf =-0.996
f=265,275