Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.5
Page 1 / 6
Unit Circle Approach ; Properties of Trig Functions
Unit Circle Trig Functions
Goal: Make sure that you can list out all 6 trig functions, using the unit circle to illustrate how we
can translate between an angle, and the trig functions' definitions as ratios of sides of a right
triangle
Given this unit circle
Write out the definition of
All 6 trig functions (as ratios
of the sides of the triangle
defined by the point (a,b)
Trig Functions of General Angles
A point on the unit circle is given . Find the exact value of each of the six trigonometric functions.
Be mindful of your signs!
 1 3

1) P =   ,

2
2


2)
 2
2

,
P = 

2
2


Page 1 / 6
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.5
Page 2 / 6
The Unit Circle
Go through, and fill in the degrees (and radians) for each line, as well as the value of the listed trig
function, for all the angles drawn. Remember that we're working with the unit circle, and so you
can use those formulas for 0°, 90°, 180°, and 270°
3) Draw in degrees, radians, and the value of the Sine function, for each line that's been drawn
onto the unit circle:
Page 2 / 6
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.5
Page 3 / 6
4) Draw in degrees, radians, and the value of the Cosine function, for each line that's been drawn
onto the unit circle:
Page 3 / 6
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.5
Page 4 / 6
5) Draw in degrees, radians, and the value of the Cosecant function, for each line that's been
drawn onto the unit circle:
Are there any lines that cause problems? What problems do they cause?
Page 4 / 6
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.5
Page 5 / 6
6) Draw in degrees, radians, and the value of the Tangent function, for each line that's been
drawn onto the unit circle:
Are there any lines that cause problems? What problems do they cause?
Page 5 / 6
Algebra &Trigonometry
Sullivan & Sullivan, Fourth Edition
§ 6.5
Use The Periodic Properties of Trig Functions To Find Exact Values
Find the exact value of each given expression
7) Sin 420 
8) Cos
11
4
9) Tan
5
4
Odd-Even Properties of Trig Functions
Find the exact value of each given expression
10) Sin  420 
11) Cos 
11
4
12) Tan 
5
4
Page 6 / 6
Page 6 / 6