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SAT Multiple Choice Question(s). 4 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?

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## SAT Multiple Choice Question(s)

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**SAT Multiple Choice Question(s)**4 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) 6 cm**Essential Question: How do I use trig identities to solve**equations and verify identities? How do I use fundamental identities to verify other identities?**See pg 454**Reciprocal Identities Also work with powers…**generating the …Pythagorean Identities**(cos , sin ) a2 + b2 = c2 1 sin (cos )2 + (sin )2 = 12 cos cos2 + sin2 = 1 cos2means the same thing as(cos )2**generating the…Pythagorean Identities**cos2 + sin2 = 1 cos2 cos2 cos2 + tan2 = sec2 1**generating the…Pythagorean Identities**cos2 + sin2 = 1 sin2 sin2 sin2 cot2 + 1 = csc2**+ tan2**= sec2 1 cot2 + 1 = csc2 Pythagorean Identities cos2 + sin2 = 1 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**pg 462**Guidelines for verifying… 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.**pg 462**Guidelines for verifying… 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 factor out a GCF = sin (1 - cos2 ) Substitute w/ Pythag ID = sin (sin2 ) Multiply = sin3 Goal: Single Trig Function, if possible**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

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