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)

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?

Reciprocal Identities See pg 454 Also work with powers…

Quotient Identities

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

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

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

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

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

Ex. Simplify

Ex. Simplify

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.

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.

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

Ex #2b Verify you try…

Ex.

Another way to do #1…

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

Ex. Verify Multiply by the conjugate

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

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

What are your questions?