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Mathematics for grade 12’s

Mathematics for grade 12’s. trigonometry. Trigonometry Defined. Trigonometry (from Greek trigōnon "triangle" + metron "measure" [1] ) is part of mathematics that studies triangles and the relationships between their sides and the angles between these sides.

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Mathematics for grade 12’s

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  1. Mathematics for grade 12’s trigonometry

  2. Trigonometry Defined. Trigonometry (from Greektrigōnon "triangle" + metron "measure"[1]) is part of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves

  3. Trigonometric equations. Sine. Cosine. Tangent. Cosec (reciprocal for sine) Secant (reciprocal for cosine) Cotangent (reciprocal for tangent) These are the six equations used in trigonometry These equations are only usable in triangles and only right-angled that is.

  4. Equations Defined. This has not changed from what you learned in grade Ten(10) Sine is the opposite side divided by the hypotenuse. ( Cosine is the adjacent side over the hypotenuse ( Tangent is the opposite side over the adjacent side (. Cotangent is the adjacent side over the opposite side ( r y y x Hint: x= Adjacent side : y= Opposite side : r= Hypotenuse

  5. Double Angles. Sin 2θ=2 sin Cos 2θ= cos- sin = 1-2sin =2-1

  6. Expansion Formulas. Sin (θ+ω)= sinθcosω+cosθsinω Sin (θ-ω)= sinθcosω–cosθsinω Cos (θ+ω)= cosθcosω–sinθsinω Cos(θ-ω)=cosθcosω+sinθsinω

  7. Example one. With the knowledge you acquired (special angles) from the previous grade use it to gain understanding on this example. Given Sin( find cosθand cos2θ Pythagoras theorem Solution: = =(5(3 =25-9 =21 x= Knowing that cos has to be the adjacent side divided by the hypotenuse Cosθ= ()

  8. Example one cont. Given this: cos 2θ= -sin =(- ( =(-( =

  9. Example Two. Sin 7 =sin 4+3 sin4+3=sin4cos3+cos4sin3 =()+()( =+ =

  10. Example Three. = LHS = (change to ) = = () = LHS=RHS

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