Transcript

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TOPIC ANALYSIS

Trigonometry

Harpreet Cheema

Simardeep Samra

Harpreet Tatla

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Grades

7

9

11 F

12 Pre Cal

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12 F

11 Pre Cal

10 A & W 10 Found & Pre Cal

11 A & W

12 A & W

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Our Track….7

9

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11 A&W 11 F

10 A&W

12 F12 A&W

11 PRE CAL10 F & PRE CAL

12 PRE CAL

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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.

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Grade 8Pythagorean 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)

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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. A tangent to a circle is perpendicular to the radius at the point of tangency A 90

B

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Grade 10 A & W• The Pythagorean

Theorem

• Sine, Cosine and Tangent Ratios

• Solving Right Triangles

only

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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

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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.

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Grade 10 Found & Pre Cal

• Sine, Cosine Ratios & Tangent Ratio

• Solving Right Triangles

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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

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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)

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Grade 12 Foundations• Sinusoidal functions in which

Represent data Describe the characteristics Graph data Interpret data Contextual problem

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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…

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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…

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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.

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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……….

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Grade 12 Pre CalEquation 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…

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Grade 12 Pre Cal • Trigonometric identities in which.

Reciprocal identities (sin θ= 1/sec θ) Quotient identities (tanθ = sin θ / cos θ ) 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) sin 2θ

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Questions????


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