1. Trigonometry Review

2. Objectives Convert between radians and degrees
Calculate values of trigonometric functions
Apply trig identities in computing values of trig functions

3. Radians In Calculus, we use radians for all solutions.
Converting from degrees to radians
multiply by π / 180
Converting from radians to degrees
multiply by 180 / π

4. Examples Change 120° to radians Change π/10 to degrees
120° × π /180°
=2π/3
Change π/10 to degrees
π /10 × 180° / π
= 18°

5. Basic Trig Identities

6. Deriving Other Identities

7. Deriving Other Identities

8. Unit Circle
π/6
π/4
π/3
π/2 0°
30°
45°
60°
90°
sinθ 1
cosθ

10. Example
Solve in [0,2π).

11. Example
Solve in [0,2π).

12. Example Solve in [0,2π). [30°,180°) U [210°,360°)
interval c
f(c)
(0,30) 20 +
(30,180) 90 -
(180,210)
200
(210,360)
300
[30°,180°) U [210°,360°)
[π/6, π) U [7 π/6,2 π)

13. Period and Amplitude y=a f (bx) where f is a trig function
amplitude: |a|
if it has an amplitude (sine and cosine)
period:
2 π/ |b| for sine, cosine, secant and cosecant
π/ |b| for tangent and cotangent

14. Examples y=3sin(4x) y=5tan(6x) amplitude period 3 2 π /4 = π/2 none
π/6

15. Homework
Handout