Test Day Day Sign Up for a problem from the study guide Test Day Day Sign Up for a problem from the study guide. First come first serve!!!We will do these 1 by 1 on the board Standards Covered MCC9‐12.N.VM.10 (+) Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. MCC9‐12.A.REI.9 (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). MCC9‐12.A.REI.8(+)Represent a system of linear equations as a single matrix equation in a vector variable. MCC9 ‐ 12.A.REI.9 (+) Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

AccPreCalc Lesson 6 Angles/ The Unit Circle (aM3 43) Essential Question: How can I use circles and degrees to understand the unit circle? What makes an angle positive or negative? What are conterminal angles? How can angle measures be greater than 180 degrees? Standards: Extend the domain of trigonometric functions using the unit circle MCC9 ‐ 12.F.TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π /3, π /4 and π /6, and use the unit circle to express the values of sine, cosine, and tangent for π ‐ x, π +x, and 2 π ‐ x in terms of their values for x, where x is any real number.

New Vocabulary Acute Angles- between 0 and 9 degrees Right angles- 90 degrees Obtuse angles- between 90 and 180 degrees Straight angles- are equal to 180 degrees Complementary angles- 2 angles whose sum is 90 degrees Supplementary angles- 2 angles whose sum is 180 degrees coterminal angles- angles that have the same terminal ray

Important formulas D = diameter r = radius D = 2r or 1.2 D = R

Eratosthenese He is best known for being the first person to calculate the circumference of the earth. Pi ≈ 3.142 Note: pi is irrational this means π cannot be expressed exactly as a ratio of any two integers (fractions such as 22/7 and other rational numbers are commonly used to approximate π, but no ratio of integers can be its exact value). Pi = c / d

More Formulas We know pi = C / d Since d = 2r Proof: We know pi = C / d Since d = 2r Pi = C/ 2r Multiply both sides by 2r to get: 2 pi r = C Q.E.D C = 2 pi r Where C = Circumference And r = radius

Area of a Circle A = ∏ r2 Where A = area of a circle And r = radius Example: A = ∏ r2 Where A = area of a circle And r = radius r = 7 A = ∏ r2 A = ∏ (49)

pi = c / d A = pi r2 Formulas on one page c = 2 pi r d = 2r or r = (1/2) d A = pi r2 c = 2 pi r

Practice Problem We also know C = 2 pi r since r = 7 C = 2 (7) pi C = 14 pi inches Given: Area of a circle = 49 pi in2 Find: circumference we know A = pi r2 so, 49 pi = pi r2 divide both sides by pi to get 49 = r2 take the square root of both sides to get r = 7 in

Θ ≈ 53 degrees Θ is a central angle Arc If you go counter clockwise you get a Positive angle. If you go clock wise you get a negative angle.

Coterminal angles coterminal angles- angles that have the same terminal ray 270 degrees and -90 degrees are coterminal angles

Quadrants

Let's say we have an angle β = 600 degrees This puts us in Q3 360 degrees is once around then we have 270 degrees left to go coterminal angles 600 degrees 240 degrees -120 degrees 960 degrees You add or subtract 360 to get a coterminal angle

Arc measure = central angle measure