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Trigonometry maths methodology

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James Modisha
James Modisha

This document discusses simplifying trigonometric expressions using CAST diagrams, identities, and co-ratios. It aims to teach learners how to simplify expressions using these methods. It first reviews prior knowledge of trigonometric ratios, the theorem of Pythagoras, and trigonometric sides. It then introduces the CAST diagram to identify positive and negative trigonometric ratios. It discusses co-ratios and trigonometric identities that can be used to simplify expressions, such as tanx = sinx/cosx. Examples are provided to simplify expressions using these techniques.

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TRIGONOMETRY SIMPLIFYING TRIGONOMETRIC EXPRESSIONS
AIMS AND OBJECTIVES The aim of the lesson: To teach learners how to simplify trigonometric expressions using the CAST diagram. To teach learners how to simplify trigonometric expressions using identities and Co-ratios
PRIOR KNOWLEDGE In grade you learnt about the theorem of Pythagoras, the trigonometric ratios and the names of the sides on a right angle. Recap Questions 1. State the theorem of Pythagoras 2. Define sin x, cos x and tan x in terms of their sides 3. Name the sides of the triangle.
PRIOR KNOWLEDGE Solve for x using the theorem of Pythagoras. Revision Theorem of Pythagoras: 2 + 2 = 2 , where c is the hypotenuse. = ＄ ＄ =
PRIOR KNOWLEDGE 駒 = ＄ = ＄ = ＄ =
THE CAST DIAGRAM This CAST diagram helps us to identify whether our trigonometric ratios are positive or negative.
CAST DIAGRAM AND TRIGONOMETRIC RATIOS. Use the CAST diagram to write the trigonometric ratios in terms of x Sin (180属+x)= -Sin x Cos (360属-x)= Cos x Tan (90属+x)= -tan x Co-ratios 90属 is a special angle that has a unique effect to Cos and Sin.
CO-RATIOS (90属x) =Cos x 駒 90属 + = sin This effect is applicable with the angle 270属 as well. What will be the answer: (90属+x) = ?? (270属 )= ??
TRIGONOMETRIC IDENTITIES ＄ = 2 + 2 = 1 Therefore, 2 = 1- 2 And 2 = 1- 2
SIMPLIFYING A TRIGONOMETRIC EXPRESSION
CLASSWORK 1. In which Quadrants are the following positive: Sin 慮 Cos 慮 Tan 慮 2. Express the following in terms of 慮: Sin (90属+ 慮) Tan (180属- 慮) Cos (360属- 慮)
CLASSWORK 3. Simplify the expressions ﾂ x cos 360属 x tan 180属 x 歎 cos(180属 x) The end.

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Trigonometry maths methodology

  • 2. AIMS AND OBJECTIVES The aim of the lesson: To teach learners how to simplify trigonometric expressions using the CAST diagram. To teach learners how to simplify trigonometric expressions using identities and Co-ratios
  • 3. PRIOR KNOWLEDGE In grade you learnt about the theorem of Pythagoras, the trigonometric ratios and the names of the sides on a right angle. Recap Questions 1. State the theorem of Pythagoras 2. Define sin x, cos x and tan x in terms of their sides 3. Name the sides of the triangle.
  • 4. PRIOR KNOWLEDGE Solve for x using the theorem of Pythagoras. Revision Theorem of Pythagoras: 2 + 2 = 2 , where c is the hypotenuse. = ＄ ＄ =
  • 5. PRIOR KNOWLEDGE 駒 = ＄ = ＄ = ＄ =
  • 6. THE CAST DIAGRAM This CAST diagram helps us to identify whether our trigonometric ratios are positive or negative.
  • 7. CAST DIAGRAM AND TRIGONOMETRIC RATIOS. Use the CAST diagram to write the trigonometric ratios in terms of x Sin (180属+x)= -Sin x Cos (360属-x)= Cos x Tan (90属+x)= -tan x Co-ratios 90属 is a special angle that has a unique effect to Cos and Sin.
  • 8. CO-RATIOS (90属x) =Cos x 駒 90属 + = sin This effect is applicable with the angle 270属 as well. What will be the answer: (90属+x) = ?? (270属 )= ??
  • 9. TRIGONOMETRIC IDENTITIES ＄ = 2 + 2 = 1 Therefore, 2 = 1- 2 And 2 = 1- 2
  • 11. CLASSWORK 1. In which Quadrants are the following positive: Sin 慮 Cos 慮 Tan 慮 2. Express the following in terms of 慮: Sin (90属+ 慮) Tan (180属- 慮) Cos (360属- 慮)
  • 12. CLASSWORK 3. Simplify the expressions ﾂ x cos 360属 x tan 180属 x 歎 cos(180属 x) The end.