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a powerpoint presentation on triginometry

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  1. 1. Made by:BHAVUN CHHABRA10TH - B
  2. 2.  Trigonometry is the study and solution ofTriangles. Solving a triangle means finding the value of each of its sides and angles.The following terminology and tactics will be important in the solving of triangles. Pythagorean Theorem (a2+b2=c2). Only for right angle triangles Sine (sin), Cosecant (csc or sin-1) Cosine (cos), Secant (sec or cos-1) Tangent (tan), Cotangent (cot or tan-1) Right/Oblique triangle
  3. 3. us e Since a triangle has three ten sides, there are six ways to adjacent o divide the lengths of the hyp sides Each of these six ratios has a name (and an abbreviation)  The ratios depend on the Three ratios are most used: shape of the triangle (the opposite  sine = sin = opp / hyp  cosine = cos = adj / hyp angles) but not on the size  tangent = tan = opp / adj e The other three ratios are nus ote adjacent  cosecant= cosec= hyp/ opp hyp  secant= sec= hyp/ adj  cotangent = cot = adj/opp opposite
  4. 4. THE SIDE OPPOSITE TO THE ANGLE angle opposite opposite oppositeangle angle angle opposite OP PO SIT E SID E
  5. 5. THE SIDE ADJACENT TO THE ANGLE angleangle angleadjacent angle t nec a da t nec a da j j ADJACENT
  6. 6. THE LONGEST SIDE se enuhy pot e h yp e nus ote nu hy pot se hyp o te n use HY PO TE NU SE
  7. 7. THREE TYPES TRIGONOMETRICRATIOS There are 3 kinds of trigonometric ratios we will learn. sine ratio cosine ratio tangent ratio
  8. 8. sine ratio θFor any right-angled triangle Opposite side Sinθ = hypotenuses
  9. 9. θFor any right-angled triangle Adjacent Side Cosθ = hypotenuses
  10. 10. θFor any right-angled triangle Opposite Side tanθ = Adjacent Side
  11. 11. Reciprocal Identities 1 1 1 cot θ = secθ = cscθ = tan θ cosθ sin θQuotient Identities sin θ cosθ tan θ = cot θ = cosθ sin θPythagorean Identities sin θ + cos θ = 1 tan θ + 1 = sec θ 1 + cot θ = csc θ 2 2 2 2 2 2Negative-Number Identities sin( −θ ) = − sin θ cos( −θ ) = cosθ tan( −θ ) = − tan θ
  12. 12.  Work with one side at a time. We want both sides to be exactly the same. Start with either side Use algebraic manipulations and/or the basic trigonometric identities until you have the same expression as on the other side.
  13. 13. cot x sin x = cos xLHS = cot x sin x and RHS = cos x cos x = ⋅ sin x sin x = cos x Since both sides are the same, the identity is verified.
  14. 14.  Start with the more complicated side Try substituting basic identities (changing all functions to be in terms of sine and cosine may make things easier) Try algebra: factor, multiply, add, simplify, split up fractions If you’re really stuck make sure to: Change everything on both sides to sine and cosine.