Plane trigonometry, by S.L. Loney.

EXAMPLES. 83
The only angle, between 0~ and 360~, satisfying both conditions is
77
therefore 210~, i.e.
The most general value is hence obtained by adding any multiple
of four right angles to this angle, and hence is 2n7r + 7 where n is any
positive or negative integer.
EXAMPLES. XI.
What are the most general values of 0 which satisfy the equations,
1.,,/3 1
1. sin 0= 2. sin sin-..
~~~~~1 ~ ~ ~ 1
4. cosO=-1. 5. cosO=2 ~. 6. cos= ---
2' 2 /2'
7. tanO=^/3. 8. tanO=-l. 9. cot =l.
2
10. sec 0=2. 11. cosec 0. 12. sin20=1.
1 1
13. cos2=4. 14. tan2=. 15. 4sin20=3.
4 3 4
16. 2cot20=cosec2 0. 17. sec20=3
18. What is the most general value of 0 that satisfies both of the
equations
cOSO= - and tan = 1?
19. What is the most general value of 0 that satisfies both of the
equations
cot0= -/3 and cosec = -2?
1 1
20. If cos (A - B) =, and sin(A +B)=, find the smallest positive
values of A and B and also their most general values.
2
21. If tan (A - B) = 1, and sec (A +B) = -, find the smallest positive
values of A and B and also their most general values.
6-2