Engineering Mechanics

(^8) „„„„„ A Textbook of Engineering Mechanics
4.
1
cosec
sin
c
b
== θ
θ
5.
1
sec
cos
c
a
==θ
θ
6.
cos 1
cot
sin tan
a
b
θ
===θ
θθ

7. The following table shows values of trigonometrical functions for some typical angles:

angle 0° 30° 45° 60° 90°

sin 0

1

2

1

2

3

2

1

cos 1

3

2

1

2

1

2

0

tan 0

1

3

1 3 ∞

or in other words, for sin write

0° 30° 45° 60° 90°

0

2

1

2

2

2

3

2

4

2

0

1

2

1

2

3

2

1

for cos write the values in reverse order ; for tan divide the value of sin by cos for the

respective angle.

8. In the first quadrant (i.e., 0° to 90°) all the trigonometrical ratios are positive.


9. In the second quadrant (i.e., 90° to 180°) only sin θ and cosec θ are positive.


10. In the third quadrant (i.e., 180° to 270°) only tan θ and cot θ are positive.


11. In the fourth quadrant (i.e., 270° to 360°) only cos θ and sec θ are positive.


12. In any triangle ABC,

sin sin sin

abc

A BC

==

where a, b and c are the lengths of the three sides of a triangle. A, B and C are opposite

angles of the sides a, b and c respectively.

13. sin (A + B) = sin A cos B + cos A sin B


14. sin (A – B) = sin A cos B – cos A sin B


15. cos (A + B) = cos A cos B – sin A sin B


16. cos (A – B) = cos A cos B + sin A sin B

17.

tan tan

tan ( )

1 – tan. tan

A B

AB

A B

+

+=

18.

tan – tan

tan ( – )

1 tan. tan

A B

AB

A B

=

+

19. sin 2A = 2 sin A cos A