Download Day V 4.4

Math Analysis
Day V.
Trigonometric Functions of Any Angle (4.4)
10/11/11
He who is devoid of the power to forgive is devoid of the power to love. Dr. Martin Luther King, Jr.,
(1929 – 1968), an American clergyman, activist, and prominent leader in the African-American Civil
Rights Movement
You can use trigonometric functions to model and solve real life problems, like modeling the average
daily temperature in a city.
Goal 1 - To evaluate trigonometric functions of any angle
I. Introduction
Life does not always give us unit circles.
Why can’t r ≤ 0?
Standard 2.1 - Students know the definition of sine and cosine as y-and x-coordinates of points on the
unit circle
Standard 5.1 - Students know the definitions of the tangent and cotangent functions.
Standard 6.1 - Students know the definitions of the secant and cosecant functions.
Since r = any value, we have generalized trigonometry definitions
sin  =
csc  =
cos  =
sec  =
tan  =
cot  =
Let’s play “Name that Quadrant”
I
sin  =
cos  =
tan  =
sec  =
csc  =
cot  =
II
III
IV
Example 1 - Evaluating Trigonometric Functions
1. Let (-12, -5) be a point on the terminal side of . Find the sine, cosine, and tangent of .
2. Let (3, 1) be a point on the terminal side of . Find the sine, cosine, and tangent of .
Your Turn
1. Let (-5, 2) be a point on the terminal side of . Find the sine, cosine, and tangent of .
2. Let (3, -7) be a point on the terminal side of . Find the sine, cosine, and tangent of .
Where am I?
sin   0 and cos   0
Your Turn
sin   0 and tan   0
sec   0 and cot   0
Example 2 - Evaluating Trigonometric Functions
If sin  = ½ and tan   0, find the exact value of cos .
Your Turn
1. If cos  = -4/5 and  is in Quadrant II, find the exact value of sin .
2. If csc  = 4/1 and cot  < 0, find the exact value of cos .
______________________________________________is an angle that lies on the x- or y-axis.
Example 3 - Trigonometric Functions of Quadrantal Angles
Find the cos  of the four quadrantal angles.
Goal 2 - To use reference angles to evaluate trigonometric functions
Standard 9.1 - Students compute, by hand, the values of the trigonometric functions at various standard points.
II. Reference Angles
______________________________________is the acute angle formed by the ___________________
of  in standard position and the ___________________________________________ axis.
Quadrant II
Quadrant III
Quadrant IV
Example 4 - Finding Reference Angles
 = 210
 = 4.1
Your Turn
1. θ = 309
2. θ = -149
3. θ = 7/4
4. θ = 11/3