IGCSE/GCSE Mathematics - 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)

• 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!

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Drafted by Bonnie (Mathematics)