1 / 13

AS Core 2 Trigonometry

AS Core 2 Trigonometry. Created by : Ali V Ali. Measuring Angles : In Degrees or Radians. . 360 o. The angle, , can be measured in degrees. This represents the turn required to move from one line to the other in the direction shown.

bob
Download Presentation

AS Core 2 Trigonometry

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. AS Core 2Trigonometry Created by : Ali V Ali

  2. Measuring Angles : In Degrees or Radians  360o The angle, , can be measured in degrees. This represents the turn required to move from one line to the other in the direction shown. This turn is measured in degrees. Degrees are a unit measuring turning where 360o is a full turn.

  3. Radians is another measure for angles. This time you represent the angle as the distance point A moves around the circumference of an imaginary circle. A If we imagine a circle of radius 1 unit, then a full turn would be a full circle and the point A moves would be the same as the circumference of the circle • 360o = 2 radians (or 2 c) • 1o = 2 c 360o • 1 c = 360o 2

  4. Uses of radians L Here we have a sector draw with angle . This sector has an arc length of L and an area of A. r Area,A  r In radians … In degrees … Length of arc, L L = (2 r)  360o Area of sector, A A = (r 2)  360o L = (2 r)  = r  2 A = (r2)  = ½ r2 2

  5. Hypotenuse Opposite Adjacent sine  = opposite ÷ hypotenuse cosine  = adjacent ÷ hypotenuse tangent  = opposite ÷ adjacent

  6. Some Standard Solutions … x 0o 45o x Hypotenuse = Adjacent Opposite = 0 sin 0o = 0 cos 0o = 1 tan 0o = 0 Adjacent = Opposite = x Hypotenuse = x2 sin 45o = 1/2 cos 45o = 1/2 tan 45o = 1 30o 60o x x 60o 60o 90o x For 30o Hypotenuse = x Opposite = x Adjacent = x 3 2 2 sin 30o = 1 cos 30o = 3 tan 30o = 1 2 23 For 60o Hypotenuse = x Adjacent = x Opposite = x 3 2 2 sin 60o = 3 cos 60o = 1 tan 60o = 3 2 2 Hypotenuse = Opposite Adjacent = 0 sin 90o = 1 cos 90o = 0 tan 90o = undefined

  7. 90o 90o Opposite = + Adjacent = + Opposite = + Adjacent = - 180o 0o 180o 0o 270o 270o 90o 90o Opposite = - Adjacent = - Opposite = - Adjacent = + 180o 0o 180o 0o 270o 270o

  8. + + - - - + - + - + - + Images from BBC AS Guru

  9. CAST Diagram

  10. Solve : sin x = 0.5 for the range 0 ≤ x ≤ 360o  x = arcsin 0.5 = 30o but sin is positive in two quadrants so x = 30o or (180 – 30)=150o

  11. Solve : sin x = 0.5 for the range 0 ≤ x ≤ 360o  x = arcsin 0.5 = 30o but sin is positive in two quadrants so x = 30o or (180 – 30)=150o

  12. The End

More Related