August 24, 2021
Triangles
Sine Graph
- When sine value is +ve:
- 1st value = sin-¹ (x)
- 2nd value = 180 - (sin-¹ (x))
- When sine value is -ve:
- 1st value = 180 - sin-¹ (x)
- 2nd value = 360 + sin-¹ (x)
Cosine Graph
- When cosine value is +ve or -ve:
- 1st Value = cos-¹ (x)
- 2nd value = 360 — cos-¹ (x)
Tan Graph
- When Tan value is +ve:
- 1st value = tan-¹ (x)
- 2nd value = 180 + tan-¹ (x)
- When Tan value is -ve:
- 1st value = 180 + tan-¹ (x)
- 2nd value = 360 + tan-¹ (x)
Non Right Angled Triangles
- Right Angled and no angles = Pythagoras
- Right angled and some angles = Trig
- If the triangle is not right angled, you may need sine/cosine rule.
Do you still remember the sine rule and cosine rule in IGCSE/GCSE Maths?
The Sine Rule
- You can only use sine rule if you have a matching pair/opposites (e.g. a and Sine A).
The Cosine Rule
- Missing Length = when you have 2 sides and an angle inbetween them.
- Missing Angle = when you have 3 sides.
- With the ambiguous case (obtuse angle), work out the missing angle but then minus from 180 to get the obtuse angle.
- Area of non-right angled triangle: ½ ab x sinC
- ab = 2 given sides, sineC = angle between the sides
- Area of right angled triangle: ½ base x height
That's the end of the topic!
Drafted by Bonnie (Mathematics)