Trigonometry is a branch of mathematics that deals with relationships between sides and angles of triangles. The document defines trigonometric ratios like sine, cosine, and tangent that relate the sides and angles of a right triangle. It also discusses trigonometric identities, angle measurement in degrees and radians, measuring angles in different quadrants, and the values of trigonometric functions for special angles.

2. BASE (B) HYPOTENUESE (H) PERPEND I CULAR (P)

5. TRIGONOMETRIC - IDENTITIES

6. √ 2 √ 3 2 Cosec  = Sec  = Cot  = Tan  = 0 1 Cos  Sin  90 ° 60 ° 45 ° 30 ° 0 ° 

7. ANGLE OF ELEVATION – α , β (OBSERVER LOOK UPWARD) β α

8. ANGLE OF DEPRESSION – α , β (OBSERVER LOOKING DOWNWARD) β α α β

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. Notational Convection 180 180 Degree Measure π x Radian measure Radian measure π x Degree measure

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. 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. 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. 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. 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. 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. 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