19 August 2023 Trigonometric ratios for special
Description: 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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slide1. 19 August 2023 Trigonometric ratios for special angles.<br>
slide2. 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<br>
slide3. 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<br>
slide4. 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<br>
slide5. 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<br>
slide6. 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<br>
slide7. 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<br>
slide8. 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<br>
slide9. 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<br>
slide10. Thank you for using resources from https://www.mathssupport.org If you have a special request, drop us an email info@mathssupport.org For more resources visit our website<br>
slide2. 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<br>
slide3. 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<br>
slide4. 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<br>
slide5. 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<br>
slide6. 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<br>
slide7. 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<br>
slide8. 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<br>
slide9. 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<br>
slide10. Thank you for using resources from https://www.mathssupport.org If you have a special request, drop us an email info@mathssupport.org For more resources visit our website<br>