Trigonometry

Pythagoras Theoram:

For all the right angled triangles “the square on the hypotenuse (c²) is equal to the sum of all the squares on the other two sides (a² + b² ).

c² = a² + b²

Trigonometrical Ratios of Acute Angle:

All angles in a right angle triangle are acute angles. (between 0 to 90 degrees).

Sine:

Cosine:

Tangent:

Tip to remember this SOH CAH TOA.

Example:

Q: Find the unknown values of :

           Sin 30 = Opposite / Hypotenuse

Sin 30 = x / 13

X = 6.5 Ans

Y² + X² = 10²

Y² = 10² –  6.5²

Y = 7.60 (Ans)

Trigonometrical Ratios of Obtuse Angles:

The trigonometric ratios of an obtuse angle (between 90 and 180 degree) can be expressed in terms of the adjacent acute angle that lies in the same straight line.

Area of Triangle:

For a known right angled triangle with any two sides given and the area.

 Area = ½ ab sin C

Area = ½ bc sin A

Area = ½ ac sin B

Sine Rule:                

                                           

It can be used when:

• Two angles and one side given.
• Two sides and one non-included angle given.

 

Cosine Rule:

a²⁼ b² = c² – (2bc cos A)

b²⁼ a² = c² – (2ac cos B)

c²⁼ a² = b² – (2ab cos C)

It can be used when:

• Three sides are given.
• Two sides and one angle is given.