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ALGEBRA II WITH TRIGONOMETRY MR. YATES UNIT 4: TRIGONOMETRY UNIT OUTLINE. I. Vocabulary Right Triangle Pythagorean Theorem Sine Cosine Tangent Ratio Trig Inverses Law of Sines Law of Cosines Unit Circle Radius Angle Standard Position Initial Side Terminal Side Degrees Radians Cartesian Coordinates (x,y) Slope Periodic Function Cycle Domain Range Maximum Minimum Amplitude Period Zeros Sine Function Cosine Function Tangent Function Asymptote II. Trig of the Right Triangle A. Know the definitions of sine, cosine, and tangent (SOHCAHTOA) B. Find the sine, cosine, or tangent of a given angle, using their definitions and a picture C. Find the sine, cosine, or tangent of a given angle, using a calculator or a trig table D. Set up a proportion to solve for a missing side E. Use inverses to find a missing angle F. Use the Pythagorean Theorem c 2 a 2 b 2 G. Draw a diagram to represent a real-world situation III. Trig of Other Triangles sin A sin B sin C a b c 2 2 2 B. Law of Cosines: c a b 2ab cosC C. Use the Law of Sines if you have two angles and a side opposite one of them A. Law of Sines: D. Use the Law of Sines if you have two sides and an angle opposite one of them E. Use the Law of Cosines if you have all sides and wish to know an angle (opposite side c) F. Use the Law of Cosines if your have two sides and the angle opposite the side you wish to know IV. Trig of the Unit Circle A. Measure angles in degrees B. Convert between degrees and radians (conversion factor is /180 or 180/) C. Draw an angle in standard position D. Find the coordinates of the point where the terminal side meets the unit circle x = cos y = sin E. Find the slope of the terminal side (tan ) F. Use the unit circle to help you with solving trig equations V. Periodic Functions A. Sketch the graph of a periodic function B. Identify the domain (possible x-values) and range (possible yvalues) of a function C. Identify the zeros, maxima, and minima of a function D. Identify the period (length, in the x-direction, of one cycle) E. Identify the amplitude (half the total height, in the y-direction) F. Use the equation of a sine, cosine or tangent function transformed to determine period and amplitude a. y = a sin (b): |a| = amplitude, 2/b = period b. y = a cos (b): |a| = amplitude, 2/b = period c. y = a tan (b): amplitude is infinite, /b = period VI. Solving Trig Equations A. Solve by doing the opposite of each operation B. Use the unit circle to identify multiple angles that have the same sine, cosine, or tangent, to find multiple solutions C. Solve by graphing the function and the value it’s supposed to equal on the calculator, and finding points of intersection Homework Assignment Date __________________ Name ________________________ 5… 4… 3… 2… 1 You may review your notes, the unit outline, and/or your book, to help you below. 5 Skills You Have Learned List them by skill name or example 4 Vocab Words You Know Define them in your own words without looking in a glossary 3 Examples of Questions You Can Do Write three algebraic challenges (can be taken from classwork) along with worked-out solutions, showing all work 2 Skills You Still Struggle With List them by skill name or example 1 Vocab Word You Are Unfamiliar With Just list the word