1. SAT Multiple Choice Question(s)
4 cm
6 cm
The figure above shows how a rectangular piece of paper is rolled into the shape of a cylinder. If it is assumed that the 4-centimeter sides of the rectangle meet with no overlap, what is the area, in square centimeters, of the base of the cylinder?
(a)
(b)
(c)
(d)
(e)

2. How do I use fundamental identities to verify other identities?
Essential Question: How do I use trig identities to solve equations and verify identities?
How do I use fundamental identities to verify other identities?

3. Reciprocal Identities
See pg 454
Also work with powers…

4. Quotient Identities

5. generating the … Pythagorean Identities
(cos , sin )
a2 + b2 = c2 1
sin 
(cos )2 + (sin )2 = 12
cos 
cos2 + sin2 = 1
cos2 means the same thing as (cos )2

6. generating the… Pythagorean Identities
cos2 + sin2 = 1
cos2
cos2
cos2 1
+ tan2
= sec2

7. generating the… Pythagorean Identities
cos2 + sin2 = 1
sin2
sin2
sin2
cot2
+ 1
= csc2

8. Pythagorean Identities
cos2 + sin2 = 1 1
+ tan2
= sec2
+ 1
cot2
= csc2
These are very important!
You can also manipulate them…

9. manipulating the Pythagorean Identities
cos2 + sin2 = 1
- cos2
- cos2
sin2 = 1 - cos2
cos2 + sin2 = 1
- sin2
- sin2
cos2 = 1 - sin2

10. Ex. Simplify

11. Ex. Simplify

12. Guidelines for verifying…
pg 462
1.) Work with one side of the equation. (The complicated side first).
2.) Look for opportunities to factor an expression, add fractions, square a binomial, or create a monomial denominator.

13. Guidelines for verifying…
pg 462
3.) Look for opportunities to use the identities.
4.) If the preceding guidelines do not help, try converting all terms to sines and cosines.
5.) Try something! Even making an attempt that leads to a dead end gives insight.

14. Ex. Verify sin  - cos2  sin =sin = sin  (1 - cos2 )
factor out a GCF
= sin  (1 - cos2 )
Substitute w/ Pythag ID
= sin  (sin2 )
Multiply
= sin3 
Goal: Single Trig Function, if possible

15. Ex #2b Verify you try…

16. Ex.

17. Another way to do #1…

18. Ex. Verify sin(t) + cot(t) cos(t)= csc(t) Write in terms of sin or cos
Multiply
Add, common denominator
Substitute
Substitute

19. Ex. Verify
Multiply by the conjugate

20. Strategies to use when verifying… factoring
Difference of Two Squares b)
trinomial

21. Ex. #6 Factor Write in terms in one function. *Substitute
*Collect like terms
*Factor

22. What are your questions?