Schaum's Outline of Trigonometry

Front Cover
McGraw Hill Professional, Dec 21, 1998 - Mathematics
5 Reviews

Updated to match the emphasis in today's courses, this clear study guide focuses entirely on plane trigonometry. It summarizes the geometry properties and theorems that prove helpful for solving trigonometry problems. Also, where solving problems requires knowledge of algebra, the algebraic processes and the basic trigonometric relations are explained carefully. Hundreds of problems solved step by step speed comprehension, make important points memorable, and teach problem-solving skills. Many additional problems with answers help reinforce learning and let students gauge their progress as they go.

 

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Contents

Angles and Applications
1
Trigonometric Functions of a General Angle
11
Trigonometric Functions of an Acute Angle
28
Solutions of Right Triangles
41
Practical Applications
56
Reduction to Functions of Positive Acute Angles
69
Variation and Graphs of the Trigonometric Functions
78
Basic Relationships and Identities
92
Sum Difference and Product Formulas
115
Oblique Triangles
120
Area of a Triangle
139
Inverses of Trigonometric Functions
149
Trigonometric Equations
159
Complex Numbers
168
Geometry
181
INDEX
214

Trigonometric Functions of Two Angles
101

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Common terms and phrases

Popular passages

Page 118 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Page 182 - A trapezoid is a quadrilateral with exactly one pair of parallel sides. The parallel sides are the bases.
Page 169 - By actual multiplication their product is rr' [cos ф cos ф' — sin ф sin ф' + (sin ф cos ф' + cos ф sin </'')}. By Trigonometry, this may be written rr' [cos (ф + ф') + z sin (ф + ф')]. Therefore, the modulus of the product of two complex numbers is the product of their moduli ; and the amplitude of the product is the sum of their amplitudes.
Page 10 - With respect to a rectangular coordinate system, an angle is said to be in standard position when its vertex is at the origin and its initial side coincides with the positive x axis.
Page 180 - When two lines are cut by a transversal, if the corresponding angles are equal, or if the interior angles on the same side of the transversal are supplementary, the lines are parallel.
Page 169 - ... and the amplitude of the quotient is the amplitude of the dividend minus the amplitude of the divisor.
Page 10 - ... These two number lines are called the horizontal axis and the vertical axis, or, together, the coordinate axes. The horizontal axis is usually referred to as the x axis and the vertical axis as the y axis, and each is labeled accordingly. Other labels may be used in certain situations. The coordinate axes divide the plane into four parts called quadrants, which are numbered counterclockwise from I to IV (see Fig. 1).
Page 27 - Thus, any function of an acute angle is equal to the corresponding cofunction of the complementary angle.
Page 184 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 182 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

About the author (1998)

Murray R. Spiegel, Ph.D., was a professor and chairman of the mathematics department at Rensselaer Polytechnic Institute, in Troy, New York. Robert E. Moyer, Ph.D. (Marshall, MN) is a professor of mathematics at Southwest Minnesota State University in, Marshall.

Frank Ayers, Ph.D., (deceased) was a professor and head of the department of mathematics at Dickinson College. Elliott Mendelson, Ph.D., (Roslyn, NY) is a professor of mathematics at Queens College.

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