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Roohi jilani

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  • 1.  "A hundred years from now, it willnot matter what kind of car I drove,what kind of house I lived in, howmuch money I had in the bank...butthe world may be a better placebecause I made a difference in thelife of a child." -- Forest Witcraft
  • 2.  "Education would be much moreeffective if its purpose was to ensurethat by the time they leave schoolevery boy and girl should know howmuch they do not know and beimbued with a lifelong desire toknow it." -- William Haley
  • 3.  "One looks back with appreciation tothe brilliant teachers, but withgratitude to those who touched ourhuman feelings. The curriculum is somuch necessary material, butwarmth is the vital element for thegrowing plant and for the soul of thechild." -- Carl Jung
  • 4.  There are two goodreasons to be ateacher – June andJuly.
  • 5.  "We spend the first twelvemonths of our childrens livesteaching them to walk and talk,and the next twelve years tellingthem to sit down and shut up."
  • 6.  "A statistician can have his headin an oven and his feet in ice, andhe will say that on the averagehe feels fine."
  • 7. • I have heard that parallellines do meet, but they arevery discrete
  • 8. BY:Mrs.ROOHI JILANI
  • 9. Measuring Angles : In Degrees or RadiansθThe angle, θ, can bemeasured in degrees. Thisrepresents the turn requiredto move from one line to theother in the direction shown.This turn is measured indegrees. Degrees are a unitmeasuring turning where 360ois a full turn.360o
  • 10. If we imagine a circle ofradius 1 unit, then a fullturn would be a fullcircle and the point Amoves would be thesame as thecircumference of thecircleRadians is anothermeasure for angles.This time you representthe angle as thedistance point A movesaround thecircumference of animaginary circle.A⇒360o= 2π radians (or 2π c)⇒1o= 2π c360o⇒1 c= 360o2π
  • 11. θrrLength of arc, LL = (2π r) θ360oArea of sector, AA = (πr 2) θ360oL = (2π r) θ = r θ2πA = (πr2) θ = ½ r2θ2πIn degrees …In radians …Here we have a sectordraw with angle θ. Thissector has an arclength of L and an areaof A.LArea,AUses of radians
  • 12. 1. Convert from degrees to radians1. 30o2. 145o3. 500o4. -60o2. Convert from radians to degrees1. 2/3 π rads2. 7/5 π rads3. -5/8 π rads4. 0.5 rads
  • 13. Calculate length of the arc and areas for these sectors,a)b)c)Radius = 4cmθ = 2/9 πRadius = 6.3cmθ = 3/7 πRadius = 14cmθ = 4.1Note : angles in radians
  • 14. AdjacentOppositeHypotenusesine θ = opposite ÷ hypotenusecosine θ = adjacent ÷ hypotenusetangent θ = opposite ÷ adjacent
  • 15. 0o90o45o60o60o60o30oHypotenuse = AdjacentOpposite = 0sin 0o= 0 cos 0o= 1 tan 0o= 0Hypotenuse = OppositeAdjacent = 0sin 90o= 1 cos 90o= 0 tan 90o=undefinedAdjacent = Opposite = xHypotenuse = x√2sin 45o= 1/√2 cos 45o= 1/√2 tan 45o= 1xxxxxFor 60oHypotenuse = xAdjacent = x Opposite = x √32 2sin 60o= √3 cos 60o= 1 tan 60o= √32 2For 30oHypotenuse = xOpposite = x Adjacent = x √32 2sin 30o= 1 cos 30o= √3 tan 30o= 12 2 √3Some Standard Solutions …
  • 16. θ(deg)0 30 45 60 90θ(rads)0 π6π4π3π2sin θ 0 ½ 1√2√321cos θ 1 √321√2½ 0tan θ 0 1√31 √3 -
  • 17. 0o180o90o270o0o180o90o270o0o180o90o270o0o180o90o270oOpposite = +Adjacent = +Opposite = +Adjacent = -Opposite = -Adjacent = -Opposite = -Adjacent = +
  • 18. ++++++- -----Images from BBC AS Guru
  • 19. Sin + All +Tan + Cos +CAST Diagram
  • 20. Sin + All +Tan + Cos +Solve : sin x = 0.5 for the range 0 ≤ x ≤ 360o∴ x = arcsin 0.5 = 30obut sin is positive in two quadrants sox = 30oor (180 – 30)=150o
  • 21. Solve : sin x = 0.5 for the range 0 ≤ x ≤ 360o∴ x = arcsin 0.5 = 30obut sin is positive in two quadrants sox = 30oor (180 – 30)=150o
  • 22. Find all the angles (in degrees) in the given range1. Sin x = - ½ for the range 0 ≤ x ≤ 360o2. Cos 2x = √3/2 for the range -360o≤ x ≤ 360o3. Tan (2x+40o) = √3 for the range -180o≤ x ≤ 180oFind all the angles (in radian) in the given range1. Sin x = √3/2 for the range 0 ≤ x ≤ 2π2. Cos 2x = -1/2 for the range -2π ≤ x ≤ 2π3. Tan (2x+ ½π) = 1 for the range -π ≤ x ≤ π
  • 23.  A physicist and an engineer are in a hot-airballoon. Soon, they find themselves lost in acanyon somewhere. They yell out for help:"Helllloooooo! Where are we?" 15 minutes later, they hear an echoing voice:"Helllloooooo! Youre in a hot-air balloon!!" The physicist says, "That must have been amathematician." The engineer asks, "Why do you say that?" The physicist replied: "The answer wasabsolutely correct, and it was utterly useless."