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Review of Trigonometry

Review of Trigonometry. Appendix D.3. 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

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Review of Trigonometry

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  1. Review of Trigonometry Appendix D.3

  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

  3. terminal ray x (0, 0) initial ray Standard position of an angle 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

  4. Measuring Angles Positive angles measured counterclockwise Negative angles measured clockwise

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

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

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

  8. Common 1st Quadrant Angles

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

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

  11. Reciprocal Identities

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

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

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

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

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

  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)

  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

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

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

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

  22. Homework Exercises for Appendix D.3: #1-7 all, 11-19 all, 27-35 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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