19 August 2023 Trigonometric ratios for special

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19 August 2023 Trigonometric ratios for special

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19 August 2023 Trigonometric ratios for special angles. Look at this isosceles right-angled triangle. A B C 1 1 c We let the equal sides have length 1. Using Pythagoras theorem, the 3rd side is c2 12 12 c2 2 Now look at the

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19 August 2023 Trigonometric ratios for special angles.

Look at this isosceles right-angled triangle. A B C 1 1 c We let the equal sides have length 1. Using Pythagoras’ theorem, the 3rd side is c2 = 12 + 12 c2 = 2

Now look at the trigonometric ratios for this triangle A B C 1 1 Take any angle, say B. Label the sides h o a opposite hypotenuse adjacent hypotenuse opposite adjacent

Look at this equilateral triangle. A B C 2 2 Let the sides be 2 cm. You will see why 2 is a convenient length. We will take only one triangle to work Trig ratios don’t depend on the size of the triangle, so we can let the sides be any convenient length. 2 Divide the triangle into 2 equal right angled triangles. 1 1

Now look at this right-angled triangle, which is half the equilateral triangle. A B 2 1 Using Pythagoras’ theorem, the 3rd side is a2 = 22 - 12 a2 = 3 a 22 = a2 + 12

A B 2 1 Now look at the trigonometric ratios for this triangle Label the sides for this angle opposite hypotenuse adjacent hypotenuse opposite adjacent h o a

Trigonometric ratios for special angles Summary sin cos tan 0 On top of the angles write down the numbers 0 - 4 Square root the number on top and divide by 2 for sine Write for cosine the same values but in inverse order For tangent, divide the value of sine by cosine

We are given the side adjacent to the angle and we want to find the length of the opposite side, so we use: h o a S O H C A H T O A Find the exact value of x in this triangle First label the sides Trigonometric ratios for special angles

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19 August 2023 Trigonometric ratios for special

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