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Most schools use SOHCAHTOA and formula triangles to teach trigonometry. I am opposed to this method for a number of reasons.
1. Knowledge vs understanding - Using SOHCAHTOA in the shape of formula triangles relies on students remembering three separate formula triangles. Students often don't remember them because they find trigonometry to be an abstract part of Maths.
2. Covering up the part of the formula triangle that the question has asked you to find does not promote a solid Mathematical understanding. For example, the student doesn't know why they are covering up the part of the formula triangle that the question has asked them to find.
3. At GCSE level, algebraic manipulation and rearranging formula is important for students that are targeting the top grades. Using formula triangles does nothing to promote these skills.
4. SOHCAHTOA only works for right-angled triangles. In some cases, the triangle in question will be an isosceles or a scalene triangle.
I am in favour of using the sine and cosine rules to teach trigonometry for the following reasons:
1. The sine and cosine rules can be proved. Some students need to see a visual proof to believe that a formula will work every time.
2. The sine and cosine rules encourage students to think. They will need to decide whether the sine or the cosine rule is the best rule to use to find the length or the angle in question
3. The sine rule requires students to rearrange formulae. These skills will enhance a students ability to change the subject of a formula and solve challenging mathematical problems usually seen towards the end of higher tier GCSE papers.
4. The sine and the cosine rules can be used to find the lengths and/or angles for any type of triangle. Thus, teaching this method eliminates the need for SOHCAHTOA altogether.
5. The sine and cosine rules are on the formula sheet in the exam. Thus, even if you cannot remember the rules by heart, providing you have practised using them prior to sitting the exam, you will be able to use them skilfully on the day. However, if you haven't practised using them, the formulae will mean nothing to you when given to you in the exam.
