Topic/Skill Topic:
Definition/Tips
Trigonometry Example
1. Exact 0° 30° 45° 60° 90°
Values for sin 0 1 √2 √3 1
Angles in 2 2 2
Trigonometry cos 1 √ 3 √2 1 0
2 2 2
tan 0 1 1 √3 ----
√3
2. Sine Rule Use with non right angle triangles.
Use when the question involves 2 sides
and 2 angles.
For missing side:
a b
= x 5.2
sin A sin B =
sin 85 sin 46
For missing angle:
sin A sin B 5.2× sin 85
= x= =3.75 cm
a b sin 46
There is an ambiguous case (where there
are two potential answers)
sin θ sin 85
=
1.9 2.4
1.9 ×sin 85
sin θ= =0.789
2.4
−1
To find the two angles, use sine to find one, θ=sin ( 0.789 )=52.1 °
and then subtract your answer from 180
to find the other answer.
3. Cosine Rule Use with non right angle triangles.
Use when the question involves 3 sides
and 1 angle.
For missing side:
2 2 2
a =b +c −2 bccosA
2 2 2
x =9.6 +7.8 −¿
For missing angle: x=11.8
b2 +c 2−a 2
cos A=
2 bc
Mr A. Coleman Glyn School
Definition/Tips
Trigonometry Example
1. Exact 0° 30° 45° 60° 90°
Values for sin 0 1 √2 √3 1
Angles in 2 2 2
Trigonometry cos 1 √ 3 √2 1 0
2 2 2
tan 0 1 1 √3 ----
√3
2. Sine Rule Use with non right angle triangles.
Use when the question involves 2 sides
and 2 angles.
For missing side:
a b
= x 5.2
sin A sin B =
sin 85 sin 46
For missing angle:
sin A sin B 5.2× sin 85
= x= =3.75 cm
a b sin 46
There is an ambiguous case (where there
are two potential answers)
sin θ sin 85
=
1.9 2.4
1.9 ×sin 85
sin θ= =0.789
2.4
−1
To find the two angles, use sine to find one, θ=sin ( 0.789 )=52.1 °
and then subtract your answer from 180
to find the other answer.
3. Cosine Rule Use with non right angle triangles.
Use when the question involves 3 sides
and 1 angle.
For missing side:
2 2 2
a =b +c −2 bccosA
2 2 2
x =9.6 +7.8 −¿
For missing angle: x=11.8
b2 +c 2−a 2
cos A=
2 bc
Mr A. Coleman Glyn School
