1 / 22

Sines, Cosines and Tangents

Sines, Cosines and Tangents. Of angles over 90 0. For Right Angled Triangles. 8cm. H. O. 4 cm. 30 0. Sin x = O / H. A. Sin 30 0 = 4 / 8 = 0.5. What about angles over 90 0 ?. What about angles over 90 0 ?. 30 0. Angles measured anti clockwise from horizontal. If angle is 150 0.

lanza
Download Presentation

Sines, Cosines and Tangents

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Sines, Cosines and Tangents Of angles over 900

  2. For Right Angled Triangles 8cm H O 4 cm 300 Sin x = O/H A Sin 300 = 4/8 = 0.5

  3. What about angles over 900?

  4. What about angles over 900? 300 Angles measured anti clockwise from horizontal

  5. If angle is 1500 180 - 150 1500 Sin1500 = Sin300!!!!!!!!! Sin1500 = 0.5 300 300

  6. 300 and 1500 are related angles Anyone else in the family?

  7. 180 + 30 = 2100 What about angles over 1800? 300 210 is in the same family as 30 and 180 sin300 = 0.5, sin1500 = 0.5 - 0.5 Sin 2100 =

  8. 210 is more of a cousin! Any more relations?

  9. Related Angles so far 1500 300 360 – 30 = 3300 2100 3300 is the final relation

  10. But which side of the family is 330? Sin300 and Sin1500 = 0.5 Sin3300 = -0.5 Sin2100 = -0.5

  11. Finding all the relations There are 4 related angles (usually) Less than 900 Between 900 and 1800 a0 180 – a a0 360 - a 180 + a Between 1800 and 2700 Between 2700 and 3600

  12. (Neat Wee Diagram) 900 Introducing the NWD ii i Less than 900 Between 900 and 1800 a0 180 – a 00 1800 iv iii (3600) 180 + a 360 - a 4 Quadrants Between 1800 and 2700 Between 2700 and 3600 Each contains a related angle 2700

  13. i ii Easiest when starting in Quadrant 1 Finding relations using NWD a0 180 – a iv iii (Acute angle) 180 + a 360 - a i 700 Relations of 700 ii 180 – 70 = 1100 iii 180 + 70 = 2500 iv 360 – 70 = 2900

  14. Positive or Negative? Looking at the relations from earlier i ii Sin300 and Sin1500 = 0.5 iii iv Sin2100 and Sin330 = -0.5 Quadrants?

  15. i ii + + Adjusting the NWD a0 180 – a iv - - iii 180 + a 360 - a + i 500 Relations of 500 + ii 180 – 50 = 1300 - iii 180 + 50 = 2300 - iv 360 – 50 = 3100

  16. 0.5 How about cosine? Related AnglesCosine 600 1200 2400 3000 -0.5 -0.5 0.5 Cosine also has related angles i and iv are positive ii and iii are negative

  17. 1 And Tangent? Related AnglesTangent 450 1350 2250 3150 -1 1 -1 Tangent also has related angles i and iii are positive ii and iv are negative

  18. Sin Cos Sin Cos - S Only Sin + i A All + + ii + + Tan Tan - Further NWD Adjustment a0 180 – a + Sin Sin Cos Cos Only Tan + iv T - C - Only Cos+ iii + - Tan Tan 180 + a 360 - a - + Not so Neat! Sorted A bit better

  19. dair A S eldom i ii NWD Final Version a0 180 – a iv iii 180 + a 360 - a T alks C rap

  20. 0.64 0.77 0.84 0.64 -0.77 -0.84 (180 – 40) -0.64 - 0.77 0.84 (180 +40) -0.64 0.77 -0.84 (360 – 40)

  21. Relations from non acute angles Ex 2300 Quad iii 900 so 180 + a = 2300 a = 500 A S i ii 180 – a a0 can easily find rest of relations 00 1800 iv T C iii 180 – 50 = 1300 180 + a 360 - a 360 – 50 = 3100 2700

  22. Relations from non acute angles Ex 3300 Quad iv 900 so 360 - a = 3300 a = 300 A S i ii 180 – a a0 can easily find rest of relations 00 1800 iv T C iii 180 – 30 = 1500 180 + a 360 - a 180 + 30 = 2100 2700

More Related