Relationship between ratios of some angles

- Complementary angles, α and 90^o – α: 

- Suplementary angles, α and 180^o - α: 

- Opposite angles, α and – α:

- Angles whose difference is 180^o, α and 180^o + α:

- Angles greater than 360^o. If x is the remainder when we divide it by 360^o , then

 

Example: if you know that sin 65^o = 0,9, calculate cos 25^o , sin 295^o, sin 425^o , sin 115^o and sin 245^o .
· cos 25^o = sin 65^o = 0,9
· sin 295^o = sin (- 65^o )= - sin 65^o = - 0,9
· sin 425^o = sin 65^o = 0,9
· sin 115^o = sin (180^o - 65^o )= sin 65^o = 0,9
· sin 245^o = sin (180^o + 65^o )= -sin 65^o = -0,9

NOTE: you can memorise this table:

 

 

Exercise: Calculate without a calculator:

a) sin 150^o

b) cos 225^o

c) cosec(7π/6)

d) tan (-495^o)

 

 

 

Solutions: a)  1/2; b) -√2/2; c) -2; d) 1