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1 Review of Trigonometry Appendix D.3

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2 After this lesson, you should be able to: work in radian measure find reference angles use and recreate the unit circle to find trig values of special angles recognize and sketch the graphs of sine, cosine and tangent use the Pythagorean trig identities and reciprocal identities to simplify trig expressions solve basic trig equations

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3 Angles initial ray on x-axis acute angles angles between 0 and /2 radians obtuse angles angles between /2 and radians co-terminal angles angles that share the same terminal ray Ex: /2 and -3 /2 initial ray terminal ray Standard position of an angle (0, 0) x

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4 Measuring Angles Positive angles measured counterclockwise Negative angles measured clockwise

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5 Radian Measure Radian measure of a central angle in the unit circle is the length of the arc of the sector. r = 1 Unit circle r s = r circle with radius r The length of the sector Arc Length is

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6 Definitions of Trig Functions x y r (x,y) Circular Function Definitions

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7 Quadrant Signs for Trig Functions Quad I: All trig functions are + Quad II: Sine and cosecant are + Quad III: Tangent and cotangent are + Quad IV: Cosine and secant are +

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8 Common 1 st Quadrant Angles Degrees0°30°45°60°90° Radians Sin Cos Tan

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9 Unit Circle Function Definitions 1 Unit circle x y r = 1

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0° 360 ° 30 ° 45 ° 60 ° 330 ° 315 ° 300 ° 120 ° 135 ° 150 ° 240 ° 225 ° 210 ° 180 ° 90 ° 270 ° For a positive angle. r = 1 Unit Circle with Special Angles Remember: x = cos , y = sin

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11 Reciprocal Identities

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12 Trigonometric Identities & Formulas Note: Those written in blue should be memorized.

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13 Graph of Sine Graph the function y = sin x over the interval [-2 , 2 ]. State its amplitude, period,domain and range. x y

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14 Graph of Cosine Graph the function y = cos x over the interval [-2 , 2 ]. State its amplitude, period,domain and range. x y

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15 Graph of Tangent Graph the function y = tan x over the interval [-2 , 2 ]. State its period,domain and range. x y

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16 Practice with Conversions Example: Convert -34 /15 to degree measure. Example: Convert 850° to exact radian measure.

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17 Practice with Trig Functions Example: Given a point on the terminal side of in standard position, find the exact value of the six trig. functions of . P (-4, -3)

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18 Practice with Trig Functions Example: Given the quadrant and one trigonometric function value of in standard position, find the exact value of the other five trig. functions. A. Quadrant I; tan = 5

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19 Practice with Trig Functions B. Quadrant III; cot = 1

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20 Solving Basic Trig Equations Example 1 Solve the equation without using a calculator.

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21 Solving Basic Trig Equations Example 2 Solve the equation without using a calculator.

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22 Homework Exercises for Appendix D.3: #1-7 all, all, odd Appendix D.3 can be found online at the textbook site and also on the CD provided with your text.

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