Trigonometry Essentials Practice Workbook with Answers

AUTHOR: Chris McMullen earned his Ph.D. in physics from Oklahoma State University and currently teaches physics at Northwestern State University of Louisiana. He developed the Improve Your Math Fluency series of workbooks to help students become more fluent in basic math skills.

WHAT TO EXPECT: This is a workbook designed to offer plenty of practice with essential skills. It is not a textbook designed to teach trigonometry, but a workbook designed to supplement a student’s instruction in trigonometry. Examples and a brief description of the concepts are included to serve as a quick refresher and a guide. If you need more instruction, you should use this workbook in combination with a textbook. The last chapter involves applications of trig identities, which is a challenging topic that will mostly interest more advanced students. A few chapters are intended to help students memorize the trig functions of common angles like 30, 150, or 315 degrees, which will be especially useful for students who may take exams without a calculator (that’s the case with the MCAT and many math and science courses). There may be more practice than many students need, which is much better than having too little practice. Any extra pages may be helpful for teachers or parents with multiple children.

DESCRIPTION: This Trigonometry Essentials Practice Workbook with Answers provides ample practice for developing fluency in very fundamental trigonometry skills. Every problem can be answered without a calculator, which is very helpful for students who aren’t allowed to use a calculator. This is the case in some trig and physics courses, as well as some standardized exams (like the MCAT).

CONTENTS: This workbook is conveniently divided up into 11 chapters so that students can focus on one trigonometry skill at a time. Skills include the following:

• converting between degrees and radians;
• expressing sine, cosine, tangent, secant, cosecant, and cotangent as fractions by looking at right triangles;
• solving for unknown sides and angles in 45°-45°-90° and 30°-60°-90° right triangles;
• determining the sine, cosine, tangent, secant, cosecant, and cotangent of multiples of 30° and 45° up to 360° (working with both degrees and radians);
• practice finding the reference angle for angles in Quadrants II, III, and IV;
• finding the inverse trig functions;
• applying the law of sines and the law of cosines to solve for unknown sides and angles in acute and obtuse triangles;
• solving problems with trig identities (like the angle sum and difference formulas);
• and solving algebraic equations that feature basic trig functions.

EXAMPLES: Each section begins with a few pages of instructions for how to solve the problems followed by some examples. These examples should serve as a useful guide until students are able to solve the problems independently.

ANSWERS: Answers to exercises are tabulated at the back of the book. This helps students develop confidence and ensures that students practice correct techniques, rather than practice making mistakes.

PHOTOCOPIES: The copyright notice permits parents/teachers who purchase one copy or borrow one copy from a library to make photocopies for their own children/students only. This is very convenient if you have multiple children/students or if a child/student needs additional practice.

INTRODUCTION: An introduction describes how parents and teachers can help students make the most of this workbook. Students are encouraged to time and score each page. In this way, they can try to have fun improving on their records, which can help lend them confidence in their math skills.

Chris McMullen is a physics instructor at Northwestern State University of Louisiana. He earned his Ph.D. in phenomenological high-energy physics (particle physics) from Oklahoma State University in 2002. Originally from California, he earned his Master's degree from California State University, Northridge, where his thesis was in the field of electron spin resonance. As a physics teacher, Dr. McMullen observed that many students lack fluency in fundamental math skills. In an effort to help students of all ages and levels master basic math skills, he has published this Improve Your Math Fluency Series of math workbooks on arithmetic, fractions, algebra, and trigonometry.