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Trigonometry: Basics
Trigonometry: Formulas
Differentiation Rules
Integration Rules
For Students:
Basic Trigonometric Functions
Definitions
Relationship Between Functions
1
2
3
4
Relationship Between Degress and Radians
5
1 rad = 150°/π = 57.295779513082320876798154814105°
6
1° = π/180 rad = 0.017453292519943295769236907684886 rad
Trigonometric Functions in Four Quadrants
The angle θ described
counterclockwise
from positive X-axis is considered
positive
.
This diagram shows the trigonometric functions with
POSITIVE
values in each quadrant.
Graph of Functions
Negative Angles
7
sin (
-θ
) = - sin
θ
8
csc (
-θ
) = - csc
θ
9
cos (
-θ
) = cos
θ
10
sec (
-θ
) = sec
θ
11
tan (
-θ
) = - tan
θ
12
cot (
-θ
) = - cot
θ
Angles More Than 90°
13
sin (
90+θ
) = sin
θ
14
csc (
90+θ
) = csc
θ
15
cos (
90+θ
) = - cos
θ
16
sec (
90+θ
) = - sec
θ
17
tan (
90+θ
) = - tan
θ
18
cot (
90+θ
) = - cot
θ
19
sin (
180+θ
) = - sin
θ
20
csc (
180+θ
) = - csc
θ
21
cos (
180+θ
) = - cos
θ
22
sec (
180+θ
) = - sec
θ
23
tan (
180+θ
) = tan
θ
24
cot (
180+θ
) = cot
θ
25
sin (
270+θ
) = - sin
θ
26
csc (
270+θ
) = - csc
θ
27
cos (
270+θ
) = cos
θ
28
sec (
270+θ
) = sec
θ
29
tan (
270+θ
) = - tan
θ
30
cot (
270+θ
) = - cot
θ
Values of Trigonometric Functions
θ°
θ rad
sin θ
cos θ
tan θ
0°
0
0
1
0
15°
π/12
(√6 - √2)/4
(√6 + √2)/4
2 - √3
30°
π/6
½
½√3
(√3)/3
45°
π/4
½√2
½√2
1
60°
π/3
½√3
½
√3
75°
5π/12
(√6 + √2)/4
(√6 - √2)/4
2 + √3
90°
π/2
1
0
±∞
other
other
See Table
See Table
See Table
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