Trig Identities

1. Chapter5
Section5.1–FundamentalIdentities

2. Reciprocal Identities
1.
2.
3.
4.
5.
6.
θ
θ
csc
1
sin =
θ
θ
sec
1
cos =
θ
θ
cot
1
tan =
θ
θ
sin
1
csc =
θ
θ
tan
1
cot =
θ
θ
cos
1
sec =

3. Quotient Identities
θ
θ
θ
cos
sin
tan =
θ
θ
θ
sin
cos
cot =

4. Pythagorean Identities
NEW!!
θθ 22
sectan1 =+
1sincos 22
=+ θθ
θθ 22
csc1cot =+

5. Simplify:
xxx 23
cossinsin + xxx 23
cossinsin +

6. Simplify:
x
xx
2
sin
)1)(sec1(sec −+
x
xx
2
sin
)1)(sec1(sec −+

7. Simplify:
x
x
x
x
cos
sin
sin1
cos
−
− x
x
x
x
cos
sin
sin1
cos
−
−

8. Simplify:
xxx coscotsin +xxx coscotsin +

9. Simplify:
x
x
x
xx
cos
sin1
sin1
cossin +
−
−

10. Simplify:
x
x
x
x
sec1
csc
sec1
csc
−
+
+

11. Ticket out the Door
• On a separate sheet of paper, explain the
humor that goes along with this picture!

12. Homework
Worksheet (odds)