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TOPIC ANALYSIS Trigonometry Harpreet Cheema Simardeep Samra Harpreet Tatla 1

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Grades 7 7 9 9 11 F 12 Pre Cal 8 8 12 F 11 Pre Cal 10 A & W 10 A & W 10 Found & Pre Cal 10 Found & Pre Cal 11 A & W 12 A & W 2

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Our Track…. 7 7 9 9 8 8 11 A&W 11 F 10 A&W 12 F 12 A&W 11 PRE CAL 10 F & PRE CAL 12 PRE CAL 3

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Grade 7 Develop and apply a formula for determining the area of rectangle.( b * h) Illustrate and explain how the area of a rectangle can be used to determine the area of a triangle.( ½ * b * h ) Identify and plot points in the four quadrants of a Cartesian plane. 4

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Grade 8 Pythagorean theorem Solve Pythagorean Problems Measure of the third side of right triangles Model, explain, concretely, pictorially the Pythagorean theorem Solve a given problem that involves Pythagorean triples e.g. ( 3, 4, 5 ) or ( 5, 12, 13) 5

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Grade 9 6

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Grade 10 A & W The Pythagorean Theorem Sine, Cosine and Tangent Ratios Solving Right Triangles only 7

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Grade 11 A& W Solve a contextual problem that involves angles of elevation or angles of depression. Solve a contextual problem that involves two or three right triangles, using the primary trigonometric ratios 8

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Grade 12 A & W Sine law and cosine law. Excluding the ambiguous case.(which are included in grade 11 Pre cal. and Foundation.) Describe the use of the sine law and cosine law in construction, industrial, commercial and artistic applications. 9

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Grade 10 Found & Pre Cal Sine, Cosine Ratios & Tangent Ratio Solving Right Triangles 10

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Difference between 10 A & W and Foundation Almost same but…. In A & W Still developing the concept of right triangles and Pythagorean Theorem. Applying similarity to right triangles Generalizing patterns from similar right triangle(set of similar right triangles, that the ratios of the length of the side opposite to the length of the side adjacent are equal) Relates every example somehow with trades 11

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Grade 11 Foundations Cosine law and the sine law. Including the ambiguous case. In which they.. Draw a diagram to represent a problem that involves the cosine law or sine law. Explain, concretely, pictorially or symbolically, whether zero, one or two triangles exist, given two sides and a non-included angle. Solve a problem involving the sine and cosine laws that requires the manipulation of a formula. No reference angle (which are in Pre cal) 12

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Grade 12 Foundations Sinusoidal functions in which Represent data Describe the characteristics Graph data Interpret data Contextual problem 13

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Grade 11 Pre Cal Angles in Standard position Reference angle Determine the quadrant in which a given angle in standard position terminates. Illustrate that the points on Cartesian plane P ( x, y), P (−x, y), P (−x,− y) and P (x,− y) are points on the terminal sides of angles in standard position that have the same reference angle. cont… 14

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Grade 11 Pre Cal Three primary trigonometric ratios for angles from 0° to 360° in standard position. Determine the exact value of the sine, cosine or tangent of a given angle with a reference angle of 30º, 45º or 60º. Describe patterns in and among the values of the sine, cosine and tangent ratios for angles from 0° to 360°. cont… 15

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Grade 11 Pre Cal Cosine law and sine law, Including the ambiguous case i.e. Describe and explain situations in which a problem may have no solution, one solution or two solutions (ASS) Using primary trigonometric ratios, a triangle that is not a right triangle. 16

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Grade 12 Pre Calculus Angles in standard position, degrees and radians. Positive or negative angles Co-terminal angles. Relationship among different systems of angle measurement. Relationship between the radian measure of an angle in standard position and the length of the arc cut on a circle of radius r, and solve problems based upon that relationship. Cont………. 17

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Grade 12 Pre Cal Equation of the unit circle. Derive the equation of the unit circle from the Pythagorean theorem. Six trigonometric ratios and expressing angles in radians and degrees Graph and analyze the trigonometric functions( sine, cosine and tangent) cont… 18

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Grade 12 Pre Cal 19

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Questions???? 20

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Solving Right Triangles Given certain measures in a right triangle, we often want to find the other angle and side measures. This is called solving the.

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