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SAT Multiple Choice Question(s)

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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  1. 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

  2. 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. See pg 454 Reciprocal Identities 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 + tan2 = sec2 1

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

  8. + tan2 = sec2 1 cot2 + 1 = csc2 Pythagorean Identities cos2 + sin2 = 1 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. 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.

  13. 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.

  14. 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

  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. What are your questions?

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