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2.3 The Sine and Cosine Ratios

2.3 The Sine and Cosine Ratios. MFM2P. E. G. 10. 20. A. B. 20. 40. A. D. Back in the day…. Yesterday, we created 3 similar triangles…. F. 15. 30. A. C. G. F. E. 20. 15. 10. 20 units. 10 units. 10 units. A. B. C. D. E. G. 10. 20. A. B. 20.

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2.3 The Sine and Cosine Ratios

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  1. 2.3 The Sine and Cosine Ratios MFM2P

  2. E G 10 20 A B 20 40 A D Back in the day…. Yesterday, we created 3 similar triangles… F 15 30 A C G F E 20 15 10 20 units 10 units 10 units A B C D

  3. E G 10 20 A B 20 OPPOSITE . HYPOTENUSE DG AF CF AF 40 A D HYP Neat Things about Ratios!!! OPP A ADJ Looking at Ratio 1 F 44.7 33.5 22.3 15 30 A C G 20 . 44.7 BE AE 10 . 22.3 15 . 33.5 = 0.45 = 0.45 = 0.45 0.45 When I look at the triangle from A

  4. HYP OPP A ADJ OPPOSITE . HYPOTENUSE The Sine Ratio! 0.45 When I look at the triangle from A There is a special name for this ratio. It is called the SINE RATIO. We can use it to solve for A. OPPOSITE . HYPOTENUSE SINA =

  5. HYP OPP A ADJ C 11 cm 37° A B SIN37° = OPPOSITE . HYPOTENUSE SINA = (11) SIN37° = 6.62 cm = The Sine Ratio! If we know A, and one side, we can calculate the length of the other side. Therefore the length of side BC is 6.6 cm

  6. E G 10 20 A B 20 AD AF ADJACENT. HYPOTENUSE AC AF 40 A D HYP Neat Things about Ratios!!! OPP A ADJ Looking at Ratio 2 F 44.7 33.5 22.3 15 30 A C G 40. 44.7 AB AE 20 . 22.3 30. 33.5 = 0.90 = 0.90 = 0.90 0.90 When I look at the triangle from A

  7. HYP OPP A ADJ ADJACENT. HYPOTENUSE The COSINE Ratio! 0.90 When I look at the triangle from A There is a special name for this ratio. It is called the COSINE RATIO. We can use it to solve for A ADJACENT . HYPOTENUSE COSA =

  8. HYP OPP A ADJ COS50° = ADJACENT. HYPOTENUSE COSA = (35) COS50° = 22.497 m = The COSINE Ratio! If we know A, and one side, we can calculate the length of the other side. C 35 m 50° A B Therefore the length of side AB is 22.5 m

  9. 11.5 Using the Sides to Solve for A If we know given the side length, we can use them to solve forA A storm caused a 13.5m lamp post to lean over. The top of the pole is now 11.5m above the ground. Find the measure of the angle between the lamp post and the ground, to the nearest degree 13.5m 13.5m

  10. Finding the Measure of an Angle 13.5 m 11.5 m x° 2nd Function sin-1 ( 11.5 13.5 ) =

  11. Are you confused?!?! If your finding this frustrating… don’t worry Its been the “COS” of frustration for many math students!

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