(^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
- 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.
- In the first quadrant (i.e., 0° to 90°) all the trigonometrical ratios are positive.
- In the second quadrant (i.e., 90° to 180°) only sin θ and cosec θ are positive.
- In the third quadrant (i.e., 180° to 270°) only tan θ and cot θ are positive.
- In the fourth quadrant (i.e., 270° to 360°) only cos θ and sec θ are positive.
- 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.
- sin (A + B) = sin A cos B + cos A sin B
- sin (A – B) = sin A cos B – cos A sin B
- cos (A + B) = cos A cos B – sin A sin B
- 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
=
+
- sin 2A = 2 sin A cos A