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
16879 Views
See similar Further Mathematics GCSE tutorsRelated Further Mathematics GCSE answers
All answers ▸The equation 3x^2 – 5x + 4 = 0 has roots P and Q, find a quadratic equation with the roots (P + 1/2Q) and (Q + 1/2P)
Show that 2cos^2(x) = 2 - 2sin^2(x) and hence solve 2cos^2(x) + 3sin(x) = 3 for 0<x<180
Rationalise and simplify (root(3) - 7)/(root(3) + 1) . Give your answer in the form a + b*root(3) where a, b are integers.
Find the coordinates of any stationary points of the curve y(x)=x^3-3x^2+3x+2