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Sine rule (note that the following two forms are actually the same sine rule just that one is an inverse of the other)
Either a ÷ sin A = b ÷ sin B = c ÷ sin C
OR sin A ÷ a = sin B ÷ b = sin C ÷ c
OR sin A ÷ a = sin B ÷ b = sin C ÷ c
Sine rule (to find one side of a triangle)
Sine rule (to find an angle in a triangle)
Cosine rule (*note that cosine rule is used when sine rule is not possible to be used to solve for side or angle in triangle)
Either a^2 = b^2 + c^2 - 2(b)(c)Cos A
OR Cos A = (b^2 + c^2 - a^2) ÷ (2bc)
I personally stick to remembering only the first form as the second form is easily derived from first form by manipulating the first form. They are anyway the same cosine rule so no need to waste effort to remember so many things.
OR Cos A = (b^2 + c^2 - a^2) ÷ (2bc)
I personally stick to remembering only the first form as the second form is easily derived from first form by manipulating the first form. They are anyway the same cosine rule so no need to waste effort to remember so many things.
Cosine rule (to find one side of a triangle)
Cosine rule (to find an angle in a triangle)
Finding area of triangle using sine rule
Take note that it is always easier to find area of triangle using the formula Area of triangle = 1/2 X base X height. However, when the height of a triangle cannot be found, we have to use this sine rule method to find area of triangle which is:
Area of triangle = (1/2)(a)(b)(sin C)
Area of triangle = (1/2)(a)(b)(sin C)
Introduction to bearings
Solving questions on bearings
The trick to solving questions on bearings is to be open-minded and think flexibly because any of all trigonometry rules (TOA, CAH, SOH, sine rule, cosine rule) and Pythagoras theorem may be used to solve a question. There may be more than one way to solve a question too. One should always seek out the simplest way if possible to solve a question. A guideline on the complexity of the solution to be used to solve a question is according to the number of marks awarded. A question awarding 3 marks and above compared to a question awarding 1 or 2 marks will require more thought as the solution may be more complex.
If one finds that he needs to write a lot of steps just to solve a 1 or 2 marks question, then he should perhaps think again whether there is an easier way to solve the same question. During exam condition, sometimes a student just have to start doing the question even if he may be using a long winded and complex way to solve the question if he really cannot think of a simpler solution for a 1 or 2 marks question. This is because time is precious and to think too long on a 1 or 2 marks question will jeopardise the other questions which the student also needs to complete. Think in terms of the big picture. It is definitely better to save an entire forest (the whole exam paper) than just save one tree (one particular question in the paper).
If one finds that he needs to write a lot of steps just to solve a 1 or 2 marks question, then he should perhaps think again whether there is an easier way to solve the same question. During exam condition, sometimes a student just have to start doing the question even if he may be using a long winded and complex way to solve the question if he really cannot think of a simpler solution for a 1 or 2 marks question. This is because time is precious and to think too long on a 1 or 2 marks question will jeopardise the other questions which the student also needs to complete. Think in terms of the big picture. It is definitely better to save an entire forest (the whole exam paper) than just save one tree (one particular question in the paper).