# 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