Easy way to understand Trigonometry

1. TRIGONOMETRY
A PRESENTATION BY:VIJAY

2. BEGINNING
BEFORE STARTING MAKE SUREYOU HAVE:
1) A NOTEBOOK
2) PEN/PENCIL
3) COMPLETE ATTENTION
MAKE SUREYOUTAKE IN NOTES DURINGTHE
PRESENTATION.

3. INDEX
INTRODUCTION
TRIGONOMETRIC RATIOS
TRIGONOMETRIC RATIOS OF SOME SPECIFIC
ANGLES
TRIGONOMETRIC RATIOS OF COMPLEMENTARY
ANGLES
TRIGONOMETRIC IDENTITIES
SUMMARY

4. INTRODUCTION
The word trigonometry is derived from the
Greek words ‘tri’ meaning three, ‘gon’
Meaning sides and ‘metron’ meaning
measure.
trigonometry is the study of relationships
between the sides and angles of a triangle.
Early astronomers used it to find out the
distances of the stars and planets from
earth.
Today it is used in engineering and physical

5. TRIGONOMETRIC RATIOS
The ratios of the sides of a right triangle are called
trigonometric ratios.Three common trigonometric ratios
are the sine (sin), cosine (cos), and tangent (tan).These
are defined for acute angleA below:B
AC
SIN(A)= OPPOSITE
HYPOTENUSE
COS(A)= ADJACENT
HYPOTENUSE
TAN(A)=OPPOSITE
ADJACENT
In these definitions, the terms opposite, adjacent, and hypotenuse refer to
the lengths of the sides.

7. OTHER TRIGONOMETRIC RATIOS
Cosecant(A) = Cos(A) = Hypotenuse = 1
Opposite Sin(A)
Secant(A) = Sec(A) = Hypotenuse = 1
Adjacent Cos(A)
Cotangent(A) = Cot(A) = Adjacent = 1
Opposite Tan(A)

9. TRIGONOMETRIC RATIOS OF SOME SPECIFIC ANGLES

10. TRIGONOMETRIC RATIOS OF COMPLEMENTARY ANGLES
(i) sin (90° - θ) = cos θ
(iii) tan (90° - θ) = cot θ
(v) sec (90° - θ) = csc θ
(ii) cos (90° - θ) = sin θ
(iv) cot (90° - θ) = tan θ
(vi) csc (90° - θ) = secθ
ComplementaryAngles:Two angles are said to be complementary if the
Thus θ and (90° - θ) are complementary angles.
We know there are six trigonometrical ratios in trigonometry.
The above explanation will help us to find the trigonometrical
ratios of complementary angles.

11. TRIGONOMETRIC IDENTITIES
A trigonometric identity is an equation involving trigonometric ratios of an
angle,
where the equation holds true for a defined range of values of the angle.
For the right triangle ABC, let 0°≤ A ≤ 90°
1) cos2 A + sin2 A = 1.
2) cos2 A =1 - sin2 A.
3) sin2 A =1 - cos2 A.
4) sec2 A - tan2 A = 1.
5) 1 + tan2 A = sec2 A.
6) tan2 A = sec2 A – 1.
7) cosec2 A - cot2 A = 1.
8) cot2 A + 1 = cosec2 A.
9) cot2 A = cosec2 A – 1 .

12. SUMMARY

13. Summary
The value of sin or cos never exceeds 1, but the
value of sec and cosec is always greater than or
equal to 1.

14. SUMMARY

15. TEST YOUR KNOWLEDGE
SOLUTIONS
:

16. SECOND QUESTION
(ii) cosec 31o - sec 59o
Solution: cosec 31o -
sec 59o
= cosec(90o - 59o) – sec
59o
= sec 59o - sec 59o = 0

17. THIRD QUESTION
If sec 4A = cosec (A – 20°), where 4A is an
acute angle, find the value of A.
Solution: sec 4A = cosec (90° - 4A) = cosec
cosec (A - 20°)
This means; 90° – 4A = A - 20°
Or, 110°– 4A = A
Or, 5A = 110°
Or, A = 22°