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SUPPLEMENTARY PROBLEMS

(1) Find the natural t-ratios of each of the following angles (1) 180 47' (2) 580 24' (3) 79 0 45'.

Answer :


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(2) Find the values of the trigonometric functions of q, given :

(a) cos q = - 4 / 5 (b) sin q = - 2 / 3 (c) tan q = 3 / 5 (d) sec q =

Answer : (a) Quad II : 3 / 5, - 4 / 5, - 3 / 4, - 4 / 3, - 5 / 4, 5 / 3
             Quad III : - 3 / 5, - 4 / 5, 3 / 4, 4 / 3, - 5 / 4, - 5 / 3


(3) Find the five coterminal angles for an angle of measure - 700 .

Answer : 2900 , 6500, 10100, - 4300, - 7900

(4) Find the values of t-ratios of the acute angles of the right triangle ABC, given that

(a) a = 2, c = 5 (b) b = , c = 4
Answer :



(5) Using the definitions, find the values of

(i) (iv) sec 3300

Answer :

(6) Verify the following using the tables

  1. cos 300 cos 600 + sin 300 sin 600 =

  2. 4 cos3450 - 3 cos 450 = - sin 450

  3. 4 cot2 (p / 6) - 5 sec2 (p / 4) + 6 csc2 (p / 3) - 7 cos2 (p / 2) = 10

  4. cos2300 + sin2 600 + sin2 900 + cos21800 = 7 (sin2450 + cos2 900 )

v.

(7) Find the acute angles A and B satisfying

(i) tan (A + B) = and cosec (A - B) = 2

Answer : - A = 450 or B = 150

(ii) 2 cos A tan B - 2 cos A - tan B + 1 = 0

Answer :- A = 600 or B = 450
(iii) 2 cos2 q - 2 cos q + 1 = 0

Answer :- q = 300 or 60 0
(iv) 3 tan2 q - 4 tan q + 3 = 0

Answer : - q = 300 or 600

(8) (i) Solve the right triangle ABC, given that Ð B = 900 , a = 40 cms, b = 65 cms.

Answer :- Ð A = 370 59' , Ð C = 520 1' c = 51.23 cms.

(ii) Solve the triangle ABC, given that Ð; A = 900 , AB = 36m and BC = 64 m

Answer :- Ð; C = 340 10' , Ð B = 550 50' , b = 52.95 m

(iii) Solve the triangle ABC, given that Ð A = 66 0 36' , a = 112.6 .

Answer :- Ð B = 230 24' , b = 48.73 , C = 122.7.

(9) The base of an isosceles triangle is 15.90 cms and the base angles are 540 28' . Find the equal sides and altitudes.

Answer :- 13.68 cms, altitude = 11.13 cms.

(10) A wall 15 m high and 10 m from a house. Find the length of the shortest ladder which will just touch the top of the wall and reach a window 20.5 m above the ground.

Answer : - 42.5 m.

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Index

2.1 Trigonometric Ratio of Acute Angles
2.2 Fundamental Relation between the trigonometric Ratios of an angle
2.3 Functions of General Angles or t Ratio
2.4 Tables of Trigonometric Function

Supplementary Problems

Chapter 3





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