## Schaum's Outline of TrigonometryUpdated 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

1 | |

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 |

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### Common terms and phrases

acute angle adjacent side airplane airspeed amplitude Arccos Arctan area of triangle Aresin axis central angle complex numbers cos a sin cos2 cosine cot a cot cot A sec cot2 degree mode direction equal equation esc A sec esc2 EXAMPLE Express Find the area Find the values formulas function value given angle graph groundspeed horizontal hypotenuse integer or zero law of cosines law of sines LBAC length mi/h modulus negative integer oblique triangle parallelogram perpendicular polar form principal value Prob quadrant quadrant II quotient radians real numbers rectangular form Refer to Fig reference angle required solutions resultant right triangle ABC roots sec A esc sec2 jc semiperimeter significant digits sin a cos sin2 sine Solve the triangle square units Supplementary Problems Table tan2 tan4 tangent terminal side trigonometric functions unit circle vector

### 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.