Your SlideShare is downloading. ×
0
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Trigonometry
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Trigonometry

760

Published on

a powerpoint presentation on triginometry

a powerpoint presentation on triginometry

Published in: Education
1 Comment
0 Likes
Statistics
Notes
  • Be the first to like this

No Downloads
Views
Total Views
760
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
118
Comments
1
Likes
0
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Made by:BHAVUN CHHABRA10TH - B
  • 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. 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. THE SIDE OPPOSITE TO THE ANGLE angle opposite opposite oppositeangle angle angle opposite OP PO SIT E SID E
  • 5. THE SIDE ADJACENT TO THE ANGLE angleangle angleadjacent angle t nec a da t nec a da j j ADJACENT
  • 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. THREE TYPES TRIGONOMETRICRATIOS There are 3 kinds of trigonometric ratios we will learn. sine ratio cosine ratio tangent ratio
  • 8. sine ratio θFor any right-angled triangle Opposite side Sinθ = hypotenuses
  • 9. θFor any right-angled triangle Adjacent Side Cosθ = hypotenuses
  • 10. θFor any right-angled triangle Opposite Side tanθ = Adjacent Side
  • 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.  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. 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.  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.

×