Sessional_Paper_1896 — Page 100

Class V.

97

The Arab and the Camel.

Once a camel came to the door of a tent and thrust in his nose.

Not being resisted he thrust in his feet. There being no hindrance he came half way in. After a while he got all the way in.

Then the Arab said to the camel-" This tent is too small for two." Said the camel to the Arab- "If so, you had better leave."

TRIGONOMETRY.

1. Shew that the sum of the numbers of degrees and grades contained in any angle is equal to 19

times their difference.

2. Explain the meaning of sind; and prove that sin {(2n−1) π + A}

=

sin 4.

3. While sailing west I observe two lights north of me: after sailing two miles their bearings are

60° and 30°, respectively, with my course. How far are they apart?

4. Prove geometrically, or otherwise, that-

(a) cos (A--B) = cos A cos B + sin A sin B.

(B) tan (A + B)

=

tan Atan B 1-tan A tan B

(y) sin A + sin B

2 sin

A+ B 2

COS

A-B

2

5. Find expressions for the sine and cosine of 3A in terms of the sines and cosines of A.

6. Determine cos 4 in terms of sind, when A lies between 270° and 450°.

7. Prove that--

(a) cos 4A

www.

8 cos1 4

8 cos2 A + 1.

=

cot A (1 + tan2 24).

(B) (cot A+ tan 2A)2

(y) sin (y—ẞ) sin (8~a) + sin (a-y) sin (d—ß) + sin (ẞ—a) sin (8—y) = 0.

8. Solve, giving the solution in general terms,-

=

9. Explain what is meant by A sin−1

sin x cos x

2.

a.

4'

and prove that sin-1 + cot-1 3

1 √5

10. In any triangle prove that-

A

(a) sin A + sin B + sin C 4 COS cos + cos +

(b) sin 4 sin B: sin C:: a: b: c.

:

11. Express the cosine of an angle of a triangle in terms of the sides.

Find the radius of the circle inscribed in a triangle in terms of the sides and area of the triangle.

12. Show how to solve a triangle, having given two sides and the included angle.

-

C =

Find A and B when a 21, b = 11, 34° 42′ 30′′; having given log 23010300, L tan.

72° 38′ 45′′ 10-5051500.