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

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## Murray R. Spiegel:

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

Published $\text {1968}$.

## $5 \quad$ Trigonometric Functions

### Definition of Trigonometric Functions for a Right Triangle

### Extensions to Angles which may be Greater than $90 \degrees$

### Relationship between Degrees and Radians

### Relationships among Trigonometric Functions

### Signs and Variations of Trigonometric Functions

### Exact Values for Trigonometric Functions of Various Angles

### Graphs of Trigonometric Functions

### Functions of Negative Angles

### Addition Formulas

### Functions of Angles in All Quadrants in terms of those in Quadrant $\text I$

- Trigonometric Functions of Angle plus Straight Angle
- Trigonometric Functions of Supplementary Angles

- Trigonometric Functions of Angle plus Three Right Angles
- Trigonometric Functions of Three Right Angles less Angle

### Relationships among Functions of Angles in Quadrant $\text I$

- Not documented.

### Double Angle Formulas

### Half Angle Formulas

- $5.41$: Half Angle Formula for Sine
- $5.42$: Half Angle Formula for Cosine
- $5.43$: Half Angle Formula for Tangent

### Multiple Angle Formulas

- $5.44$: Triple Angle Formula for Sine
- $5.45$: Triple Angle Formula for Cosine
- $5.46$: Triple Angle Formula for Tangent

- $5.47$: Quadruple Angle Formula for Sine
- $5.48$: Quadruple Angle Formula for Cosine
- $5.49$: Quadruple Angle Formula for Tangent

- $5.50$: Quintuple Angle Formula for Sine
- $5.51$: Quintuple Angle Formula for Cosine
- $5.52$: Quintuple Angle Formula for Tangent

### Powers of Trigonometric Functions

### Sum, Difference and Product of Trigonometric Functions

- $5.61$: Prosthaphaeresis Formula for Sine plus Sine
- $5.62$: Prosthaphaeresis Formula for Sine minus Sine
- $5.63$: Prosthaphaeresis Formula for Cosine plus Cosine
- $5.64$: Prosthaphaeresis Formula for Cosine minus Cosine

- $5.65$: Simpson's Formula for Sine by Sine
- $5.66$: Simpson's Formula for Cosine by Cosine
- $5.67$: Simpson's Formula for Sine by Cosine

### General Formulas

### Inverse Trigonometric Functions

### Principal Values for Inverse Trigonometric Functions

### Relations between Inverse Trigonometric Functions

- $5.74$: Sum of Arcsine and Arccosine
- $5.75$: Sum of Arctangent and Arccotangent
- $5.76$: Sum of Arcsecant and Arccosecant

- $5.77$: Arcsine of Reciprocal equals Arccosecant
- $5.78$: Arccosine of Reciprocal equals Arcsecant
- $5.79$: Arctangent of Reciprocal equals Arccotangent

### Graphs of Inverse Trigonometric Functions

- $5.86$: Graph of Arcsine Function
- $5.87$: Graph of Arccosine Function
- $5.88$: Graph of Arctangent Function
- $5.89$: Graph of Arccotangent Function
- $5.90$: Graph of Arcsecant Function
- $5.91$: Graph of Arccosecant Function

### Relationships between Sides and Angles of a Plane Triangle

- $5.92$: Law of Sines
- $5.93$: Law of Cosines
- $5.94$: Law of Tangents
- $5.95$: Sine of Angle of Triangle by Semiperimeter

### Relationships between Sides and Angles of a Spherical Triangle