Revision
33. Elementary trigonometry
New Chapter
34. Solution of triangles and other applications of trigonometry
Study Plan
October
22Study sections 34.1 to 34.5
Revision points
1. Semiperimeter of a triangle is denoted by s.
2. Area of a triangle is denoted by Δ or S.
3. a,b, and c represent sides BC,CA, and AB
4. Sine rule
In any Δ ABC
Sin A/a = Sin B/b = Sin C/c
5. Cosine Formulae
In any Δ ABC
Cos A = [b² + c² -a²]/2bc
Cos B = [c² +a² –b²]/2ac
Cos C = [a² + b² –c²]/2ab
6. Projection formulae
In any Δ ABC
a = b Cos C + C cos B
b= c Cos A + A Cos C
c = a Cos B + b cos A
7. Trigonometrical ratios of half of the angles of a triangle
1. Sin A/2 = √[(s-b)(s-c)/bc]
2. Cos A/2 = √[s(s-a)/bc]
3. tan A/2 = √(s-b)(s-c)/s(s-a)]
23 OctoberStudy Sections 34.6, 34.7, 34.8, 34.9,
Revision points
8. Area of a triangle
S = ½ ab Sin C = ½ bc sina = ½ ac sin B
9. Napier’s analogy
In any triangle ABC
Tan [(b-c)/2] = [(b-c)cot (A/2)]/(b+c)
10. Circumcircle of a triangle
The circle which passes through the angular points or vertices of a triangle ABC is called its circumcircle.
The centre of this circle can be found by locating the point of intersection of perpendicular bisectors of the sides. It is called circumcentre.
The circumcentre may lie within, outside or upon one of the sides of the triangle.
In a right angled triangle the cicumcentre is vertex where right angle is formed.
The radius of circumcircle is denoted by R.
R = a/(2 Sin A) = b/(2 sin B) = c/(2 sin C)
11. Inscribed circle or incircle of a triangle
It is the circle touches each of the sides of the triangle.
The centre of the inscribed circle is the point of intersection of bisectors of the angles of the triangle.
The radius of inscribed circle is denoted by r (it is called in-radius) and it is equal to the length of the perpendicular from its centre to any of the sides of the triangle.
Various formulas that give r.
In- radius ( r )= Δ/s
r = (s-a)tan (A/2) = (s-b) tan (B/2) = (s-c) tan (C/2)
r = [a sin B/2 sin C/2/(Cos A/2)
r = 4R sin (A/2) sin (B/2) sin (C/2)
Attempt Objective Type Exercises 1 to 10
October 24th34.10, 34.11
Revision points
12. Escribed circles of a triangle
The circle which touches the sides BC and two sides AB and AC produced of a triangle ABC is called the escribed circle opposite to the angle A. Its radius is denoted by r1.
Similarly r2 and r3 denote the radii of the escribed circles opposite to the angles B and C respectively.
The centres of the escribed circles are called the ex-centres.
13. Orthocentre and its distances from the angular points of a triangle
In a Δ ABC, the point at which perpendiculars drawn from the three vertices (heights) meet, it called the ortho centre of the ΔABC
Attempt objective type exercises 11 to 20
October 25th
Study 34.12 to 34.15
Revision points
14. Regular polygon and Radii of the inscribed and circumscribing circles of a regular polygon
the centre of the polygon will be the in-centre as well as circumcentre of the polygon.
15. Area of a cyclic quadrilateral
a quadrilateral is a cyclic quadrilateral if its vertices lie on a circle.
Area of cyclic quadrilateral = ½ (ab + cd) sin B
16. Ptolemy’s theorem
In a cyclic quadrilateral ABCD, AC.BD = AB.CD + BC.AD
The product of diagonals is equal to the sum of the products of the lengths of opposite sides.
17. Circum-radius of a cyclic quadrilateral
In a cyclic quadrilateral, the circumcircle of the quadrilateral ABCD is also the circumcircle of Δ ABC.
Attempt obj type exercises 21 to 30.
October 26th
Attempt obj type exercises 31 to 45.
October 27th
Attempt obj type exercises 46 to 60.
October 28th
Attempt obj type exercises 61 to 75.
October 29th
Attempt obj type exercises 76 to 90.
October 30th
Attempt fill in the blanks 1 to 15.
October 31st
Attempt fill in the blanks 16 to 31.
Practice Exercise at the end of the chapter has 21 problems you have to do these problems during the next 10 days as a part of the revision of earlier chapter. 2 problems a day will take care of all the 21 problems.
Problems of Ch. 33. Elementary trigonometry whihc you have not done so far, have to done as revision part during these 10 days.
