Why does tanx = sinx/cosx ?
This identity can easily be shown by asking the student to draw a right-angled triangle, with one of the remaing two angles labelled x, and labelling the respective oppposite, adjacent and hypotenuse sides O, A and H. Then I ask them to write down what sinx and cosx equal with respect to their diagram (O'H and A/H). I proceed to ask them to write sinx/cosx in terms of O, A and H and simplify the fraction. They will then end up with O/A, which they realise is tanx from their own diagram.I really enjoy when students ask me this as it's a chance for them to discover an impactful result on their own using some very basic maths.
SR
Answered by Shehan R. • Further Mathematics tutor
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