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Trignometary

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Trignometary

1. 1. INTRODUCTION <ul><li>Trigonometry is branch of mathematics. Which is derived from Greek Word </li></ul><ul><li>Tri three </li></ul><ul><li>Gon sides </li></ul><ul><li>Metron measure </li></ul>
2. 2. BASE (B) HYPOTENUESE (H) PERPEND I CULAR (P)
3. 3. <ul><li>T - RATIO`s </li></ul><ul><li>Sin θ = P/H = 1/Cosec θ </li></ul><ul><li>Cos θ = B/H = 1/Sec θ </li></ul><ul><li>Tan θ = P/B = Sin θ /Cos θ </li></ul><ul><li>Cosec θ = H/P = 1/Sin θ </li></ul><ul><li>Sec θ =H/B = 1/Cos θ </li></ul><ul><li>Cot θ = B/P = 1/Tan θ = Cos θ /Sin θ </li></ul>θ P B H
4. 4. Funny Way To Learn T- Ratio`s <ul><li>P B P </li></ul><ul><li>Pandit Badri Prasad </li></ul><ul><li>H H B </li></ul><ul><li>Har Har Bole </li></ul><ul><li>S C T </li></ul><ul><li>Sona Chandi Tole </li></ul>
5. 5. TRIGONOMETRIC - IDENTITIES
6. 6. √ 2 √ 3 2 Cosec  = Sec  = Cot  = Tan  = 0 1 Cos  Sin  90 ° 60 ° 45 ° 30 ° 0 ° 
7. 7. ANGLE OF ELEVATION – α , β (OBSERVER LOOK UPWARD) β α
8. 8. ANGLE OF DEPRESSION – α , β (OBSERVER LOOKING DOWNWARD) β α α β
9. 9. Measurement of Radian Angle subtended at the centre by an arc of length 1 unit in a unit circle is said to have a measure of 1 radian. 1 Radian 1 1 O A B 1 θ (r) l θ = l/r l = r θ
10. 10. Notational Convection 180 180 Degree Measure π x Radian measure Radian measure π x Degree measure
11. 11. X Y` Y FIRST QUADRANT SECOND QUADRANT THIRD QUADRANT FOURTH QUADRANT (ALL POSITIVE ) (Sin θ ,Cosec θ Positive) (90 - θ ) (90 + θ ) (180 - θ ) (180 + θ ) (270 - θ ) (270 + θ ) (360 - θ ) X` Sin (90 + θ ) = Cos θ Cos (90 + θ ) = - Sin θ (180 – θ ) = Sin θ Tan (90 + θ ) = - Cot θ (180 – θ ) = - Tan θ (180 – θ ) = - Cos θ Sin(90 – θ ) = Cos θ Cos(90 – θ ) = Sin θ Tan(90 – θ ) = Cot θ Cot(90 – θ ) = Tan θ Sec(90 – θ ) = Cosec θ Cosec(90 – θ ) = Sec θ Sin (180 + θ ) = - Sin θ (270 – θ ) = - Cos θ Cos (180 + θ ) = - Cos θ (270 – θ ) = - Sin θ Tan (180 + θ ) = Tan θ (270 – θ ) = Cot θ Sin (270 + θ ) = - Cos θ (360 - θ ) = - Sin θ Cos (270 + θ ) = Sin θ (360 – θ ) = Cos θ Tan (270 + θ ) = - Cot θ (360 – θ ) = - Tan θ ADD (Tan θ ,Cot θ Positive) (Cos θ ,Sec θ Positive) SUGAR TO COFFEE
12. 12. 0 π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 7 π 6 5 π 4 4 π 3 3 π 2 5 π 3 7 π 4 11 π 6 2 π π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 1/2 1/√2 √ 3/2 1 -1/2 -1/√2 -√3/2 -1 Sin θ 0 -1 2 -1 √ 2 - √3 2 -1 - √3 2 -1 √ 2 -1 2 0 1 2 1 √ 2 √ 3 2 1 √ 3 2 1 √ 2 1 2 0 2 π 11 π 6 7 π 4 5 π 3 3 π 2 4 π 3 5 π 4 7 π 6 π 5 π 6 3 π 4 4 π 6 π 2 π 3 π 4 Π 6 0 θ
13. 13. 0 π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 7 π 6 5 π 4 4 π 3 3 π 2 5 π 3 7 π 4 11 π 6 2 π π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 1/2 1/√2 √ 3/2 1 -1/2 -1/√2 -√3/2 -1 Cos θ 1 √ 3 2 1 √ 2 1 2 0 -1 2 -1 √ 2 - √3 2 -1 - √3 2 -1 √ 2 -1 2 0 1 2 1 √ 2 √ 3 2. 1 2 π 11 π 6 7 π 4 5 π 3 3 π 2 4 π 3 5 π 4 7 π 6 π 5 π 6 3 π 4 4 π 6 Π 2 π 3 π 4 Π 6 0 θ
14. 14. 0 π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 7 π 6 5 π 4 4 π 3 3 π 2 5 π 3 7 π 4 11 π 6 2 π π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 1/2 1/√2 √ 3/2 1 -1/2 -1/√2 -√3/2 -1 Tan θ 0 -1 √ 3 -1 - √3 ∞ √ 3 1 √ 3 0 -1 √ 3 -1 - √3 ∞ √ 3 1 1 √ 3 0 2 π 11 π 6 7 π 4 5 π 3 3 π 2 4 π 3 5 π 4 7 π 6 π 5 π 6 3 π 4 4 π 6 Π 2 π 3 π 4 Π 6 0 θ
15. 15. 0 π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 7 π 6 5 π 4 4 π 3 3 π 2 5 π 3 7 π 4 11 π 6 2 π π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 1/2 1/√2 √ 3/2 1 -1/2 -1/√2 -√3/2 -1 Cot θ ∞ - √3 -1 -1 √ 3 0 1 √ 3 1 1 √ 3 ∞ - √3 -1 -1 √ 3 0 1 √ 3 1 √ 3 ∞ 2 π 11 π 6 7 π 4 5 π 3 3 π 2 4 π 3 5 π 4 7 π 6 π 5 π 6 3 π 4 4 π 6 Π 2 π 3 π 4 Π 6 0 θ
16. 16. 0 π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 7 π 6 5 π 4 4 π 3 3 π 2 5 π 3 7 π 4 11 π 6 2 π π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 1 -1 Sec θ 2 2/√3 √ 2 -2/√3 -√2 -2 1 2 √ 3 √ 2 2 ∞ -2 - √2 -2 √ 3 -1 -2 √ 3 -√2 -2 ∞ 2 √ 2 2 √ 3 1 2 π 11 π 6 7 π 4 5 π 3 3 π 2 4 π 3 5 π 4 7 π 6 π 5 π 6 3 π 4 4 π 6 Π 2 π 3 π 4 Π 6 0 θ
17. 17. 0 π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 7 π 6 5 π 4 4 π 3 3 π 2 5 π 3 7 π 4 11 π 6 2 π π 6 π 4 π 3 π 2 4 π 6 3 π 4 5 π 6 π 1 2/√3 √ 2 2 -1 -√2 -2/√3 -2 Cosec θ ∞ -2 - √2 -2 √ 3 -1 -2 √ 3 - √2 -2 ∞ 2 √ 2 2 √ 3 1 2 √ 3 √ 2 2 ∞ 2 π 11 π 6 7 π 4 5 π 3 3 π 2 4 π 3 5 π 4 7 π 6 π 5 π 6 3 π 4 4 π 6 π 2 π 3 π 4 π 6 0 θ