1. 4.3 Trigonometry Extended: The Circular Functions
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2. Angle
Standard Position
Positive angle
(rotate counterclockwise)
Negative Angle
(rotate clockwise)

3. Coterminal Angles
Coterminal angles are angles in standard position that have a common terminal side
To find a positive or negative coterminal angle add or subtract 360°.
If the angle is measured in radians, then add/subtract 2π

4. Finding coterminal angles
Find a positive and negative coterminal angle for the given angles: 30
-150
2π/3

5. Angles and (x, y) coordinates in the Cartesian Plane

6. The point (3 , 4) is on the terminal side of angle θ
The point (3 , 4) is on the terminal side of angle θ. Evaluate the six trigonometric functions for θ.
sin θ=
cos θ=
tan θ=
csc θ=
sec θ=
cot θ=

7. You Try. The point (5,-2) is on the terminal side of angle θ
You Try! The point (5,-2) is on the terminal side of angle θ. Evaluate the six trigonometric functions for θ.
sin θ=
cos θ=
tan θ=
csc θ=
sec θ=
cot θ=

8. Trig Functions of any Angle
sin θ=
cos θ=
tan θ=
csc θ=
sec θ=
cot θ=

9. Find the six trig functions of 315°
sin 315°=
cos 315°=
tan 315°=
csc 315°=
sec 315°=
cot 315°=

10. Find sin (-210°) without a calculator:
You Try! Find cos (-210°) and cot (-210°) without a calculator:

11. Find the value of tan 3π
You Try! Find the value of sin 3π and cos 3π

12. Ex) sin θ = 3/7 and tan θ < 0
Using one trig ratio to find the others
Ex) sin θ = 3/7 and tan θ < 0

13. Unit Circle
A circle of radius 1 centered at the origin

15. Trig Functions of Real Numbers
sin t=
cos t=
tan t=
csc t=
sec t=
cot t=

16. Periodic Functions
A function y =f(t) is periodic if there is a positive number c such that f (t + c) = f(t) for all values of t in the domain of f. The smallest such number c is called the period of the function.
A periodic function repeats itself at regular intervals.
Sine and Cosine functions have period 2 π and the tangent function has period π
Find the value without a calculator of:

17. Unit Circle

18. Quiz Study Guide
Converting angles from DMS to decimal degrees( and decimal degrees to DMS)
Converting from radians to degrees (and degrees to radians)
Using the arc length formula
Finding an angle degree for a specific compass bearing
Angular and Linear Speed Problems (Unit Conversions)
Given the sin of an angle θ, find cosine of θ
Using reference triangles
Finding Positive and Negative coterminal Angles