Trigonometry/Plane

Plane trigonometry involves solving the mathematics of triangles. The law of sines and cosines are fundamental to this.

Law of sines

{\frac {a}{\sin A}}={\frac {b}{\sin B}}

{\frac {a}{\sin A}}={\frac {c}{\sin C}}

{\frac {b}{\sin B}}={\frac {c}{\sin C}}

{\text{Area}}={\frac {1}{2}}bc\sin A

{\text{Area}}={\frac {1}{2}}ab\sin C

{\text{Area}}={\frac {1}{2}}ac\sin B

This law uses the Pythagorean theorem, but this includes non-right angles.

a^{2}=b^{2}+c^{2}-2ab\cos A

b^{2}=a^{2}+c^{2}-2ab\cos B

c^{2}=b^{2}+a^{2}-2ab\cos C

s is the semi-perimeter

s={\frac {1}{2}}(a+b+c)

{\text{Area}}={\sqrt {s(s-a)(s-b)(s-c)}}

↑ Trigonometry (7th ed.), Addison Wesley, 2001, 0-321-05759-7
↑ "Trigonometry". Britannica 28: 619. (1993). University of Chicago. 0-85229-571-5.

This article is issued from Wikiversity. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.