December 16, 2015
(4.3) Trigonometric Functions of Any Angle
Objective: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
Why: Trigonometric functions of any angle allow knowledge beyond
right triangle trigonometry and opens up many applications.
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
standard position for angles:
y
positive angle: counterclockwise
x
negative angle: clockwise
coterminal angles: angles that have the same initial and
terminal sides, but different measurements.
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
a. Draw the angle in standard position.
b. Draw a positive coterminal angle. Give it's measurement.
c. Draw a negative coterminal angle. Give it's measurement.
2π
π
1. 30o
3. 2.
3
4
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
(x,y)
r
y
θ
x
r = x2 + y2
To learn about the Unit Circle.
sin θ =
cscθ =
cos θ =
sec θ =
tan θ =
cot θ =
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
Let θ be the acute angle in standard position whose terminal side
contains the point (3,4). Find the six trigonometric function of θ .
December 16, 2015
Extend the definitions in terms of x, y, and r - whether or not x any y are positive.
Let θ be the acute angle in standard position whose terminal side
contains the point (-3,5). Find the six trigonometric functions of θ .
December 16, 2015
Trig. Functions of Any Angle
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
y
P(x,y)
r
y
x
θ
sin θ =
csc θ =
cos θ =
sec θ =
tan θ =
cot θ =
x
r = x2 + y2
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
Sign Pattern for Sin, Cos, and Tan
To learn about the Unit Circle.
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
Evaluate the following without a calculator.
1. sin (7π )
6
4. sec (11π )
2
2. tan (5π )
3
5. csc (3π )
3. cos (-3π)
4
6. cot (-2π)
3
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
If sin θ= 3
7
and tan θ < 0, find cos θ and tan θ .
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
Unit Circle:
To learn about the Unit Circle.
y
(0,1)
(1,0)
(-1,0)
(0,-1)
x
December 16, 2015
Obj: To learn how to evaluate the trig. function of any angle.
(many without a calculator)
To learn about the Unit Circle.
HW:
(HR): (4.3) Pg.347: 1-3, 21-45odd