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TOPIC ANALYSIS

TOPIC ANALYSIS. Trigonometry Harpreet Cheema Simardeep Samra Harpreet Tatla. Grades. 7. 8. 9. 10 A & W. 10 Found & Pre Cal. 11 F. 11 A & W. 11 Pre Cal. 12 Pre Cal. 12 A & W. 12 F. Our Track…. 7. 8. 9. 11 PRE CAL. 10 A &W.

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TOPIC ANALYSIS

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  1. TOPIC ANALYSIS Trigonometry Harpreet Cheema Simardeep Samra Harpreet Tatla

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

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

  4. 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.

  5. 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)

  6. Grade 9 • Old curriculum SIN, COS, TAN RATIOS which are shifted to grade 10 now. • New curriculum ( only Pythagorean Theorem) Solve problems and justify the solution strategy using circle properties e.g. Atangent to a circle is perpendicular to the radius at the point of tangency A 90 B

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

  8. 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

  9. 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.

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

  11. 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

  12. 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)

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

  14. 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…

  15. 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…

  16. 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.

  17. 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……….

  18. Grade 12 Pre Cal Equationof 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…

  19. Grade 12 Pre Cal • Trigonometric identities in which. • Reciprocal identities (sin θ= 1/sec θ) • Quotient identities (tanθ = sin θ / cosθ ) • Pythagorean identities ( θ + θ = 1) • Sum or difference identities (restricted to sine, cosine and tangent) sin (A±B) • Double-angle identities (restricted to sine, cosine and tangent) sin2θ

  20. Questions????

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