Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 5

Rectangle of Length $b$ and Width $a$

 * $5.1$ Definition:Sine/Definition from Triangle


 * $5.2$ Definition:Cosine/Definition from Triangle


 * $5.3$ Definition:Tangent Function/Definition from Triangle


 * $5.4$ Definition:Cotangent/Definition from Triangle


 * $5.5$ Definition:Secant of Angle


 * $5.6$ Definition:Cosecant/Definition from Triangle

Extensions to Angles which may be Greater than $90^\circ$

 * Definition:Cartesian Coordinate System/Coordinate Plane


 * Definition:Cartesian Coordinate System/Ordered Pair


 * Definition:Cartesian Coordinate System/Ordered Pair/X Coordinate


 * Definition:Cartesian Coordinate System/Ordered Pair/Y Coordinate


 * Distance of Point from Origin in Cartesian Coordinates


 * Definition:Polar Coordinates
 * Definition:Radial Coordinate
 * Definition:Angular Coordinate


 * Definition:Cartesian Coordinate System/Quadrants


 * Definition:Cartesian Coordinate System/Quadrants/First


 * Definition:Cartesian Coordinate System/Quadrants/Second


 * Definition:Cartesian Coordinate System/Quadrants/Third


 * Definition:Cartesian Coordinate System/Quadrants/Fourth


 * $5.7$ Sine of Angle in Cartesian Plane


 * $5.8$ Cosine of Angle in Cartesian Plane


 * $5.9$ Tangent of Angle in Cartesian Plane


 * $5.10$ Cotangent of Angle in Cartesian Plane


 * $5.11$ Secant of Angle in Cartesian Plane


 * $5.12$ Cosecant of Angle in Cartesian Plane

Relationship between Degrees and Radians

 * $5.13$ Value of Radian in Degrees


 * $5.14$ Value of Degree in Radians

Relationships among Trigonometric Functions

 * $5.15$ Tangent is Sine divided by Cosine


 * $5.16$ Cotangent is Reciprocal of Tangent


 * $5.16$ Cotangent is Cosine divided by Sine


 * $5.17$ Secant is Reciprocal of Cosine


 * $5.18$ Cosecant is Reciprocal of Sine


 * $5.19$ Sum of Squares of Sine and Cosine


 * $5.20$ Sum of Squares of Sine and Cosine/Corollary 1


 * $5.21$ Sum of Squares of Sine and Cosine/Corollary 2

Signs and Variations of Trigonometric Functions

 * Shape of Sine Function


 * Shape of Cosine Function


 * Shape of Tangent Function


 * Shape of Cotangent Function


 * Shape of Secant Function


 * Shape of Cosecant Function

Exact Values for Trigonometric Functions of Various Angles

 * {| class="wikitable" style="text-align: center;"

! Angle in Degrees !! Angle in Radians !! Particular Values of Sine Function !! Particular Values of Cosine Function !! Particular Values of Tangent Function !! Particular Values of Cotangent Function !! Particular Values of Secant Function !! Particular Values of Cosecant Function
 * $0 \degrees$ || $0$ || Sine of Zero is Zero || Cosine of Zero is One || Tangent of Zero || Cotangent of Zero || Secant of Zero || Cosecant of Zero
 * $15 \degrees$ || $\dfrac \pi {12}$ || Sine of 15 Degrees || Cosine of 15 Degrees || Tangent of 15 Degrees || Cotangent of 15 Degrees || Secant of 15 Degrees || Cosecant of 15 Degrees
 * $30 \degrees$ || $\dfrac \pi 6$ || Sine of 30 Degrees || Cosine of 30 Degrees || Tangent of 30 Degrees || Cotangent of 30 Degrees || Secant of 30 Degrees || Cosecant of 30 Degrees
 * $45 \degrees$ || $\dfrac \pi 4$ || Sine of 45 Degrees || Cosine of 45 Degrees || Tangent of 45 Degrees || Cotangent of 45 Degrees || Secant of 45 Degrees || Cosecant of 45 Degrees
 * $60 \degrees$ || $\dfrac \pi 3$ || Sine of 60 Degrees || Cosine of 60 Degrees || Tangent of 60 Degrees || Cotangent of 60 Degrees || Secant of 60 Degrees || Cosecant of 60 Degrees
 * $75 \degrees$ || $\dfrac {5 \pi} {12}$ || Sine of 75 Degrees || Cosine of 75 Degrees || Tangent of 75 Degrees || Cotangent of 75 Degrees || Secant of 75 Degrees || Cosecant of 75 Degrees
 * $90 \degrees$ || $\dfrac \pi 2$ || Sine of Right Angle || Cosine of Right Angle || Tangent of Right Angle || Cotangent of Right Angle || Secant of Right Angle || Cosecant of Right Angle
 * $105 \degrees$ || $\dfrac {7 \pi} {12}$ || Sine of 105 Degrees || Cosine of 105 Degrees || Tangent of 105 Degrees || Cotangent of 105 Degrees || Secant of 105 Degrees || Cosecant of 105 Degrees
 * $120 \degrees$ || $\dfrac {2 \pi} 3$ || Sine of 120 Degrees || Cosine of 120 Degrees || Tangent of 120 Degrees || Cotangent of 120 Degrees || Secant of 120 Degrees || Cosecant of 120 Degrees
 * $135 \degrees$ || $\dfrac {3 \pi} 4$ || Sine of 135 Degrees || Cosine of 135 Degrees || Tangent of 135 Degrees || Cotangent of 135 Degrees || Secant of 135 Degrees || Cosecant of 135 Degrees
 * $150 \degrees$ || $\dfrac {5 \pi} 6$ || Sine of 150 Degrees || Cosine of 150 Degrees || Tangent of 150 Degrees || Cotangent of 150 Degrees || Secant of 150 Degrees || Cosecant of 150 Degrees
 * $165 \degrees$ || $\dfrac {11 \pi} {12}$ || Sine of 165 Degrees || Cosine of 165 Degrees || Tangent of 165 Degrees || Cotangent of 165 Degrees || Secant of 165 Degrees || Cosecant of 165 Degrees
 * $180 \degrees$ || $\pi$ || Sine of Straight Angle || Cosine of Straight Angle || Tangent of Straight Angle || Cotangent of Straight Angle || Secant of Straight Angle || Cosecant of Straight Angle
 * $195 \degrees$ || $\dfrac {13 \pi} {12}$ || Sine of 195 Degrees || Cosine of 195 Degrees || Tangent of 195 Degrees || Cotangent of 195 Degrees || Secant of 195 Degrees || Cosecant of 195 Degrees
 * $210 \degrees$ || $\dfrac {7 \pi} 6$ || Sine of 210 Degrees || Cosine of 210 Degrees || Tangent of 210 Degrees || Cotangent of 210 Degrees || Secant of 210 Degrees || Cosecant of 210 Degrees
 * $225 \degrees$ || $\dfrac {5 \pi} 4$ || Sine of 225 Degrees || Cosine of 225 Degrees || Tangent of 225 Degrees || Cotangent of 225 Degrees || Secant of 225 Degrees || Cosecant of 225 Degrees
 * $240 \degrees$ || $\dfrac {4 \pi} 3$ || Sine of 240 Degrees || Cosine of 240 Degrees || Tangent of 240 Degrees || Cotangent of 240 Degrees || Secant of 240 Degrees || Cosecant of 240 Degrees
 * $255 \degrees$ || $\dfrac {17 \pi} {12}$ || Sine of 255 Degrees || Cosine of 255 Degrees || Tangent of 255 Degrees || Cotangent of 255 Degrees || Secant of 255 Degrees || Cosecant of 255 Degrees
 * $270 \degrees$ || $\dfrac {3 \pi} 2$ || Sine of Three Right Angles || Cosine of Three Right Angles || Tangent of Three Right Angles || Cotangent of Three Right Angles || Secant of Three Right Angles || Cosecant of Three Right Angles
 * $285 \degrees$ || $\dfrac {19 \pi} {12}$ || Sine of 285 Degrees || Cosine of 285 Degrees || Tangent of 285 Degrees || Cotangent of 285 Degrees || Secant of 285 Degrees || Cosecant of 285 Degrees
 * $300 \degrees$ || $\dfrac {5 \pi} 3$ || Sine of 300 Degrees || Cosine of 300 Degrees || Tangent of 300 Degrees || Cotangent of 300 Degrees || Secant of 300 Degrees || Cosecant of 300 Degrees
 * $315 \degrees$ || $\dfrac {7 \pi} 4$ || Sine of 315 Degrees || Cosine of 315 Degrees || Tangent of 315 Degrees || Cotangent of 315 Degrees || Secant of 315 Degrees || Cosecant of 315 Degrees
 * $330 \degrees$ || $\dfrac {11 \pi} 6$ || Sine of 330 Degrees || Cosine of 330 Degrees || Tangent of 330 Degrees || Cotangent of 330 Degrees || Secant of 330 Degrees || Cosecant of 330 Degrees
 * $345 \degrees$ || $\dfrac {23 \pi} {12}$ || Sine of 345 Degrees || Cosine of 345 Degrees || Tangent of 345 Degrees || Cotangent of 345 Degrees || Secant of 345 Degrees || Cosecant of 345 Degrees
 * $360 \degrees$ || $2 \pi$ || Sine of Full Angle || Cosine of Full Angle || Tangent of Full Angle || Cotangent of Full Angle || Secant of Full Angle || Cosecant of Full Angle
 * }
 * $195 \degrees$ || $\dfrac {13 \pi} {12}$ || Sine of 195 Degrees || Cosine of 195 Degrees || Tangent of 195 Degrees || Cotangent of 195 Degrees || Secant of 195 Degrees || Cosecant of 195 Degrees
 * $210 \degrees$ || $\dfrac {7 \pi} 6$ || Sine of 210 Degrees || Cosine of 210 Degrees || Tangent of 210 Degrees || Cotangent of 210 Degrees || Secant of 210 Degrees || Cosecant of 210 Degrees
 * $225 \degrees$ || $\dfrac {5 \pi} 4$ || Sine of 225 Degrees || Cosine of 225 Degrees || Tangent of 225 Degrees || Cotangent of 225 Degrees || Secant of 225 Degrees || Cosecant of 225 Degrees
 * $240 \degrees$ || $\dfrac {4 \pi} 3$ || Sine of 240 Degrees || Cosine of 240 Degrees || Tangent of 240 Degrees || Cotangent of 240 Degrees || Secant of 240 Degrees || Cosecant of 240 Degrees
 * $255 \degrees$ || $\dfrac {17 \pi} {12}$ || Sine of 255 Degrees || Cosine of 255 Degrees || Tangent of 255 Degrees || Cotangent of 255 Degrees || Secant of 255 Degrees || Cosecant of 255 Degrees
 * $270 \degrees$ || $\dfrac {3 \pi} 2$ || Sine of Three Right Angles || Cosine of Three Right Angles || Tangent of Three Right Angles || Cotangent of Three Right Angles || Secant of Three Right Angles || Cosecant of Three Right Angles
 * $285 \degrees$ || $\dfrac {19 \pi} {12}$ || Sine of 285 Degrees || Cosine of 285 Degrees || Tangent of 285 Degrees || Cotangent of 285 Degrees || Secant of 285 Degrees || Cosecant of 285 Degrees
 * $300 \degrees$ || $\dfrac {5 \pi} 3$ || Sine of 300 Degrees || Cosine of 300 Degrees || Tangent of 300 Degrees || Cotangent of 300 Degrees || Secant of 300 Degrees || Cosecant of 300 Degrees
 * $315 \degrees$ || $\dfrac {7 \pi} 4$ || Sine of 315 Degrees || Cosine of 315 Degrees || Tangent of 315 Degrees || Cotangent of 315 Degrees || Secant of 315 Degrees || Cosecant of 315 Degrees
 * $330 \degrees$ || $\dfrac {11 \pi} 6$ || Sine of 330 Degrees || Cosine of 330 Degrees || Tangent of 330 Degrees || Cotangent of 330 Degrees || Secant of 330 Degrees || Cosecant of 330 Degrees
 * $345 \degrees$ || $\dfrac {23 \pi} {12}$ || Sine of 345 Degrees || Cosine of 345 Degrees || Tangent of 345 Degrees || Cotangent of 345 Degrees || Secant of 345 Degrees || Cosecant of 345 Degrees
 * $360 \degrees$ || $2 \pi$ || Sine of Full Angle || Cosine of Full Angle || Tangent of Full Angle || Cotangent of Full Angle || Secant of Full Angle || Cosecant of Full Angle
 * }
 * $285 \degrees$ || $\dfrac {19 \pi} {12}$ || Sine of 285 Degrees || Cosine of 285 Degrees || Tangent of 285 Degrees || Cotangent of 285 Degrees || Secant of 285 Degrees || Cosecant of 285 Degrees
 * $300 \degrees$ || $\dfrac {5 \pi} 3$ || Sine of 300 Degrees || Cosine of 300 Degrees || Tangent of 300 Degrees || Cotangent of 300 Degrees || Secant of 300 Degrees || Cosecant of 300 Degrees
 * $315 \degrees$ || $\dfrac {7 \pi} 4$ || Sine of 315 Degrees || Cosine of 315 Degrees || Tangent of 315 Degrees || Cotangent of 315 Degrees || Secant of 315 Degrees || Cosecant of 315 Degrees
 * $330 \degrees$ || $\dfrac {11 \pi} 6$ || Sine of 330 Degrees || Cosine of 330 Degrees || Tangent of 330 Degrees || Cotangent of 330 Degrees || Secant of 330 Degrees || Cosecant of 330 Degrees
 * $345 \degrees$ || $\dfrac {23 \pi} {12}$ || Sine of 345 Degrees || Cosine of 345 Degrees || Tangent of 345 Degrees || Cotangent of 345 Degrees || Secant of 345 Degrees || Cosecant of 345 Degrees
 * $360 \degrees$ || $2 \pi$ || Sine of Full Angle || Cosine of Full Angle || Tangent of Full Angle || Cotangent of Full Angle || Secant of Full Angle || Cosecant of Full Angle
 * }
 * $345 \degrees$ || $\dfrac {23 \pi} {12}$ || Sine of 345 Degrees || Cosine of 345 Degrees || Tangent of 345 Degrees || Cotangent of 345 Degrees || Secant of 345 Degrees || Cosecant of 345 Degrees
 * $360 \degrees$ || $2 \pi$ || Sine of Full Angle || Cosine of Full Angle || Tangent of Full Angle || Cotangent of Full Angle || Secant of Full Angle || Cosecant of Full Angle
 * }
 * $360 \degrees$ || $2 \pi$ || Sine of Full Angle || Cosine of Full Angle || Tangent of Full Angle || Cotangent of Full Angle || Secant of Full Angle || Cosecant of Full Angle
 * }

Graphs of Trigonometric Functions

 * $5.22$ Graph of Sine Function


 * $5.23$ Graph of Cosine Function


 * $5.24$ Graph of Tangent Function


 * $5.25$ Graph of Cotangent Function


 * $5.26$ Graph of Secant Function


 * $5.27$ Graph of Cosecant Function

Functions of Negative Angles

 * $5.28$ Sine Function is Odd


 * $5.29$ Cosine Function is Even


 * $5.30$ Tangent Function is Odd


 * $5.31$ Cosecant Function is Odd


 * $5.32$ Secant Function is Even


 * $5.33$ Cotangent Function is Odd

Addition Formulas

 * $5.34$ Sine of Sum


 * $5.34$ Sine of Difference


 * $5.35$ Cosine of Sum


 * $5.35$ Cosine of Difference


 * $5.36$ Tangent of Sum


 * $5.36$ Tangent of Difference


 * $5.37$ Cotangent of Sum


 * $5.37$ Cotangent of Difference