Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 5
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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
- $5.61$: Sine plus Sine
- $5.62$: Sine minus Sine
- $5.63$: Cosine plus Cosine
- $5.64$: 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