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The basic trigonometric functions sine, cosine and tangent are (normally) introduced as ratios on sides in a right-angled triangle in secondary schools.

But how do we introduce/explain the negative ratio when for example,cosine is more than 90 degress， where the value is negative?

Is there any good materials or ways to extend them？

CasperYC
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    This answer of mine may-or-may-not help. – Blue Sep 18 '21 at 02:07
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    I personally think using triangles to discuss trig ratios for non-acute angles is not a good idea. The unit circle definition makes more sense in this context. – ultralegend5385 Sep 18 '21 at 03:10
  • @ultralegend5385 I agree, but as an introductory lesson, I think most textbooks from Europe as well as Asia use the right-angled triangle method. Only for most able students, they would understand the unit circle. Only an opion from a maths teacher who loves reading textbooks. lol – CasperYC Sep 19 '21 at 13:00
  • I believe trig functions for non-acute angles aren't considered as something "introductory". If you mean introduction to this new concept, I think you should tell them this idea of unit circle, basically extending the triangle definition. Noticing that coordinates can be negative, in my opinion, is easier than noticing that the sides of a triangle can be negative. – ultralegend5385 Sep 19 '21 at 15:09

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