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What is the point of $\sin$ or $\cos$ or $\tan$ of an obtuse angle? Don't we use these functions to find a missing side in a right angle triangle? So why would I use it on an obtuse angle?

I have also done a unit circle.

Sebastiano
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OmarKhaled
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    Not every triangle is right angled. Some triangles even have obtuse angles. – Angina Seng Jul 10 '20 at 16:13
  • I understand that some triangles have obtuse angles but arent trig functions such as sin used to find sides of a right angle triangle? – OmarKhaled Jul 10 '20 at 16:15
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    If you go on in math, you'll find that trigonometry has a lot of uses other than, and more important than, solving triangles. – saulspatz Jul 10 '20 at 16:16
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    Right triangles are not the only application. Indeed trigonometric functions find uses in many areas of mathematics that are not obviously "geometric". As an example, the cosine function can be used to solve cubic polynomials with all real roots, without invoking complex numbers. – hardmath Jul 10 '20 at 16:17
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    Even just considering triangles, look up the law of cosines. It applies to all triangles, not just right triangles. – Joe Jul 10 '20 at 16:17
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    The trigonometric functions are defined for angles from zero to a full turn, and even several full turns, and also backwards ! They have many many uses, even outside geometry. –  Jul 10 '20 at 16:20
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    Other geometric trig formulae that apply for obtuse angles include the sine rule, the sine area rule, things like the dot product formula and the cross product magnitude formula. – Izaak van Dongen Jul 10 '20 at 16:20
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    thanks guys, I think I understand now. – OmarKhaled Jul 10 '20 at 16:27

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If all you want to do is think about right triangles then you will never encounter obtuse angles and so do not need to know about the values of the trigonometric functions at such angles. But there are triangles with an obtuse angle that you may want to study.

Moreover, the trigonometric functions appear in many contexts that do not involve triangles. They are crucial in understanding periodic phenomena. There you want to know about $\sin x$ for all possible values of $x$ (whether negative or positive, and as large as you wish). Since you have "done the unit circle" you have started studying this context.

Ethan Bolker
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