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

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

Published $1968$.

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## $5 \quad$ Trigonometric Functions

### 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/Definition from Triangle
$5.6$ 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:Angular Coordinate
$5.7$ 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

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

### 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

$5.34$ Sine of Sum
$5.34$ Sine of Sum/Corollary
$5.35$ Cosine of Sum
$5.35$ Cosine of Sum/Corollary
$5.36$ Tangent of Sum
$5.36$ Tangent of Sum/Corollary
$5.37$ Cotangent of Sum
$5.37$ Cotangent of Sum/Corollary