Engineering Mechanics

(Joyce) #1

(^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



  1. 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.


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

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

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

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

  5. 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.


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

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

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

  4. 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

=
+


  1. sin 2A = 2 sin A cos A

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