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Basic Trigonometric Functions

Definitions
Relationship Between Functions
12
34
Relationship Between Degress and Radians
51 rad = 150°/π = 57.295779513082320876798154814105°
61° = 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
7sin () = - sin θ8csc () = - csc θ
9cos () = cos θ10sec () = sec θ
11tan () = - tan θ12cot () = - cot θ
Angles More Than 90°
13sin (90+θ) = sin θ14csc (90+θ) = csc θ
15cos (90+θ) = - cos θ16sec (90+θ) = - sec θ
17tan (90+θ) = - tan θ18cot (90+θ) = - cot θ
19sin (180+θ) = - sin θ20csc (180+θ) = - csc θ
21cos (180+θ) = - cos θ22sec (180+θ) = - sec θ
23tan (180+θ) = tan θ24cot (180+θ) = cot θ
25sin (270+θ) = - sin θ26csc (270+θ) = - csc θ
27cos (270+θ) = cos θ28sec (270+θ) = sec θ
29tan (270+θ) = - tan θ30cot (270+θ) = - cot θ
Values of Trigonometric Functions
θ°θ radsin θcos θtan θ
0010
15°π/12(√6 - √2)/4(√6 + √2)/42 - √3
30°π/6½½√3(√3)/3
45°π/4½√2½√21
60°π/3½√3½√3
75°5π/12(√6 + √2)/4(√6 - √2)/42 + √3
90°π/210±∞
otherotherSee TableSee TableSee Table


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