General approach The foundation to this topic is seeing it as a continuous flow rather than a series of disjointed formulae. This section builds upon formulae learned at GCSE to develop the link between and to . This helps with the understanding of the exact values of the various trigonometric functions. The right-angled triangle can then be extended into working with the unit circle and how this relates to Pythagoras' Theorem, leading to the first of the Pythagorean identities. If this is shown as a plot then the link from here to the graphs becomes natural rather than forced. If the identities are presented visually then it will often seem less daunting and easier to recall. For solving of equations, learners are usually adept at finding the first solution but struggle with the later ones. This is often down to a reluctance to draw the graphs as they feel this is a little simplistic. However, the graphs are always a key to getting all the correct solutions. Prior knowledge Prior Knowledge from OCR J560 GCSE (9 1) Mathematics – A higher tier learner at GCSE should be able to: 6.02d Recall and use standard formulae, including Trigonometry formulae , , , sine rule , cosine rule and area of a triangle 7.02a Recognise and sketch the graphs of , , . 7.03a Identify and sketch translations and reflections of a given graph (or the graph of a given equation). e.g. . 10.03a know and apply the formula . Know, derive and apply theorem to find lengths in right-angled triangles in 2D Pythagoras’ 10.05a figures. Apply theorem in more complex figures, including 3D figures. Pythagoras’ 10.05b Know and apply the trigonometric ratios, , and and apply them to find angles and lengths in right-angled triangles in 2D figures. Apply the trigonometry of right-angled triangles in more complex figures, including 3D figures. 10.05c Know exact values of and for = 0o, 30o, 45o, 60o, 90o. Know exact values of for = 0o, 30o, 45o, 60o 10.05d Know and apply the sine rule, , to find lengths and angles. 10.05e Know and apply the cosine rule, , to find lengths and angles.
General approach The foundation to this topic is seeing it as a continuous flow rather than a series of disjointed formulae. This section builds upon formulae learned at GCSE to develop the link between and to . This helps with the understanding of the exact values of the various trigonometric functions. The right-angled triangle can then be extended into working with the unit circle and how this relates to Pythagoras' Theorem, leading to the first of the Pythagorean identities. If this is shown as a plot then the link from here to the graphs becomes natural rather than forced. If the identities are presented visually then it will often seem less daunting and easier to recall. For solving of equations, learners are usually adept at finding the first solution but struggle with the later ones. This is often down to a reluctance to draw the graphs as they feel this is a little simplistic. However, the graphs are always a key to getting all the correct solutions. Prior knowledge Prior Knowledge from OCR J560 GCSE (9 – 1) Mathematics A higher tier learner at GCSE should be able to: 6.02d Recall and use standard formulae, including Trigonometry formulae , , , sine rule , cosine rule and area of a triangle 7.02a Recognise and sketch the graphs of , , . 7.03a Identify and sketch translations and reflections of a given graph (or the graph of a given equation). e.g. . 10.03a know and apply the formula . 10.05a Know, derive and apply Pythagoras’ theorem to find lengths in right-angled triangles in 2D figures. Apply Pythagoras’ theorem in more complex figures, including 3D figures. 10.05b Know and apply the trigonometric ratios, , and and apply them to find angles and lengths in right-angled triangles in 2D figures. Apply the trigonometry of right-angled triangles in more complex figures, including 3D figures. 10.05c Know exact values of and for = 0o, 30o, 45o, 60o, 90o. Know exact values of for = 0o, 30o, 45o, 60o 10.05d Know and apply the sine rule, , to find lengths and angles. 10.05e Know and apply the cosine rule, , to find lengths and angles.
466247-pythagoras-theorem-and-trigonometry-delivery-guide.docx