# Review of Trigonometry

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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 use the Pythagorean trig identities and reciprocal identities to simplify trig expressions solve basic trig equations

Angles initial ray  on x-axis
terminal ray Standard position of an angle (0, 0) x 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

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

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

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

Quad II: Sine and cosecant are + Quad I: All trig functions are + Quad III: Tangent and cotangent are + Quad IV: Cosine and secant are +

Degrees 30° 45° 60° 90° Radians Sin  Cos  Tan 

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

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

Reciprocal Identities

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

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

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

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

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

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)

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

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

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

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

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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