39: Trigonometric ratios of 3 special angles © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

3 Special Angles "Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages" OCR MEI/OCR Module C2

3 Special Angles We sometimes find it useful to remember the trig. ratios for the angles These are easy to find using triangles. In order to use the basic trig. ratios we need right angled triangles which also contain the required angles.

3 Special Angles Consider an equilateral triangle. Divide the triangle into 2 equal right angled triangles. Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length ( You’ll see why 2 is useful in a minute ).

3 Special Angles Consider an equilateral triangle. Divide the triangle into 2 equal right angled triangles. Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length We now consider just one of the triangles. ( You’ll see why 2 is useful in a minute ).

3 Special Angles Consider an equilateral triangle. Divide the triangle into 2 equal right angled triangles. Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length. 1 2 We now consider just one of the triangles. ( You’ll see why 2 is useful in a minute ).

3 Special Angles 1 2 From the triangle, we can now write down the trig ratios for Pythagoras’ theorem gives the 3 rd side. ( Choosing 2 for the original side means we don’t have a fraction for the 2 nd side )

3 Special Angles 1 1 For we again need a right angled triangle. By making the triangle isosceles, there are 2 angles each of. We let the equal sides have length 1. Using Pythagoras’ theorem, the 3 rd side is From the triangle, we can now write down the trig ratios for

3 Special AnglesSUMMARYThe trig. ratios for are:

3 Special Angles

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3 Special Angles Consider an equilateral triangle. Divide the triangle into 2 equal right angled triangles. Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length ( You’ll see why 2 is useful in a minute ).

3 Special Angles 1 2 From the triangle, we can now write down the trig ratios for Pythagoras’ theorem gives the 3 rd side. ( Choosing 2 for the original side means we don’t have a fraction for the 2 nd side )

3 Special Angles 1 1 For we again need a right angled triangle. By making the triangle isosceles, there are 2 angles each of. We let the equal sides have length 1. Using Pythagoras’ theorem, the 3 rd side is From the triangle, we can now write down the trig ratios for

3 Special Angles SUMMARY The trig. ratios for are: