pt. I. Getting started with trigonometry -- 1. Trouncing trig technicalities -- Taking trig for a ride : what trig is -- Sizing up the basic figures -- Angling for position -- Triangulating your position -- Circling the wagons -- Understanding Trig Speak -- Defining trig functions -- Taming the radicals -- Equating and identifying -- Graphing for gold -- Describing graphing scales -- Recognizing basic graphs -- 2. Coordinating your efforts with Cartesian coordinates -- Starting out simple : plotting points -- Axes, axes, we all fall down -- Determining the origin of it all -- Plotting x versus y -- Cutting the graph into four parts -- From here to there : calculating distances -- Counting on vertical and horizontal distances -- Another slant : diagonal distances -- Using exact values or estimating distances -- Getting to the center of it all -- finding the midpoint of a line segment -- Locating the center of a circle -- Partitioning line segments further -- Pinpointing the center of a triangle -- Racing down the slope -- Slaloming slope formula -- Recognizing parallel and perpendicular lines -- Defining circles with numbers -- Centering circles at the origin -- Wandering centers -- 3. Functioning well -- Relations versus functions -- Function junction, what's your function -- Using function notation -- Determining domain and range -- In-verse functions : rhyme or reason -- Which functions have inverses -- Finding an inverse function -- Transforming functions -- Translating a function -- Reflecting like a mirror -- 4. Getting your degree -- Angles, angles everywhere : measuring in degrees -- Slicing a coordinate plane -- Looking elsewhere for degree measures -- Graphing angles in standard position -- Positioning initial and terminal sides -- Measuring by quadrants -- What's your angle? : labeling in various ways -- Using negative angle measures -- Comingling with coterminal angles -- Renaming angles : so many aliases -- 5. Dishing out the pi : radians -- What's in a radian -- Relating to a circle -- Converting degrees and radians -- HIghlighting favorites -- Making a clone of arc -- Taking chunks out of circles -- Sweeping hands -- Going out and about -- 6. Getting it right with triangles -- Sizing up right triangles -- What's so right about them -- Anatomy of a right triangle -- Demystifying the Pythagorean Theorem -- Hitting a Pythagorean triple -- Solving for a missing length -- Special right triangles -- 30-60-90 right triangles -- Isosceles right triangles --

pt. II. Trigonometric functions -- 7. Doing right by trig functions -- How trig functions work -- Right triangle's three sides -- The six ratios : relating the three sides -- The sine function : opposite over hypotenuse -- The cosine function : adjacent over hypotenuse -- The tangent function : opposite over adjacent -- Using one function to solve for another -- Similar right triangles within a right triangle -- Reciprocal functions -- The cosecant function : sine flipped upside down -- The secant function : cosine on its head -- The cotangent function : tangent, tails side up -- Identifying the most popular angles -- Determining the exact values of functions -- 8. Trading triangles for circles : circular functions -- Getting acquainted with the unit circle -- Placing points on the unit circle -- Finding a missing coordinate -- Sticking to rational coordinates -- Going full circle with the angles -- Staying positive -- Being negative or multiplying your angles -- Locating and computing reference angles -- 9. Defining trig functions globally -- Defining trig functions for all angles -- Reference angles -- Combining all the rules -- Using coordinates of circles to solve for trig functions -- Calculating with coordinates on the unit circle -- Calculating with coordinates on any circle at the origin -- Defining domains and ranges of trig functions -- Sine and cosine -- Cosecant and secant -- Tangent and cotangent -- 10. Applying yourself to trig functions -- Elevating and depressing -- Measuring tall buildings with a single bound -- Rescuing a damsel from a tower -- Determining the height of a tree -- Measuring the distance between buildings -- Measuring slope -- Spotting a balloon -- Tracking a rocket -- Measuring the view of satellite cameras -- Calculating odd shapes and maneuvering corners -- Finding the area of a triangular piece of land -- Using Heron's Formula -- Moving an object around a corner --

pt. III. Identities -- 11. Identifying basic identities -- Reciprocal identities -- Ratio identities -- Opposite-angle identities -- Pythagorean identities -- Combining the identities -- Many face of sine -- 12. Operating on identities -- Summing it up -- Overcoming the differences -- Explaining +- -- Half-angle identities -- 13. Proving identities : the basics -- Changing to sines and cosines -- Factoring -- 14. Sleuthing out identity solutions -- Fracturing fractions -- Finding a common denominator -- Multiplying by a conjugate -- Squaring both sides -- Identifying with the operations -- Adding -- Difference -- Multiplying -- Halving -- pt. IV. Equations and applications -- 15. Investigating inverse trig functions -- Notation -- Determining domain and range of inverse trig functions -- Inverse sine function -- Inverse cosine function -- Inverse tangent function -- Inverse cotangent function -- Inverse secant function -- Inverse cosecant function -- 16. Making inverse trig work for you -- Inverses -- Getting friendly with your calculator -- Changing the mode -- Interpreting notation on the calculator -- Multiplying the input -- Solving some mixed problems -- 17. Solving trig equations -- Generating simple solutions -- Factoring in the solutions -- Greatest common factor -- Factoring quadratics -- Increasing the degrees in factoring -- Factoring by grouping -- Quadratic formula -- Incorporating identities -- Multiple-angle solutions -- Squaring both sides -- Multiplying through -- solving with a graphing calculator -- 18. Obeying the laws -- Parts of triangles -- The Law of Sines -- The Law of Cosines -- Law of Cosines for SAS -- Law of Cosines for SSS -- Areas of triangles -- Finding area with base and height -- Finding area with three sides -- Finding area with SAS -- Finding area with ASA --

pt. V. The graphs of trig functions -- 19. graphing sine and cosine -- Describing amplitude and period -- formalizing the sine equation -- Translating the sine -- Graphing cosine -- Comparing cosine to sine -- Using properties to graph cosine -- Applying the sines of the times -- Sunning yourself -- Averaging temperature -- Taking your temperature -- Making a goal -- Theorizing with biorhythms -- 20. Graphing tangent and cotangent -- Determining the period -- Assigning the asymptotes -- Fiddling with the tangent -- Confronting the cotangent -- 21. Graphing other trig functions -- Identifying the asymptotes -- Using the sine graph -- Varying the cosecant -- Unveiling the secant -- Determining the asymptotes -- Sketching the graph of secant -- Fooling around with secant -- Laying out the inverse functions -- Graphing inverse sine and cosine -- Taking on inverse tangent and cotangent -- Crafting inverse secant and cosecant -- 22. Topping off trig graphs -- Basics of trig equations -- Flipping over a horizontal line -- Interpreting the equation -- Graphing with the general form -- Adding and subtracting functions -- Applying yourself to the t ask -- Measuring the tide -- Tracking the deer population -- Measuring the movement of an object on a spring -- pt. VI. The pt. of tens -- 23. Ten basic identities -- Reciprocal identities -- Ratio identities -- Pythagorean identities -- Opposite-angle identities -- Multiple-angle identities -- 24. Ten not-so-basic identities -- Product-to-sum identities -- Sum-to-product identities -- Reduction formula -- Mollweide's equations -- Appendix. Trig functions table.