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<aside> <img src="https://image.flaticon.com/icons/svg/1828/1828885.svg" alt="https://image.flaticon.com/icons/svg/1828/1828885.svg" width="40px" /> There has been numerous proofs of the Pythagoras' theorem, including Bhaskara's First and Second Proof, and Garfield's Proof
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For a given right triangle, the theorem states:
$$ \begin{alignedat}{3} c^2&=&a^2&+b^2\\ {\rm hyp}^2&=&{\rm kat_1}^2&+{\rm kat_2}^2 \end{alignedat} $$
The six trigonometric functions
$$ \sin(A)={a\over c} $$
$$ \cos(A)={b\over c} $$
$$ \tan(A)={a\over b} $$
$$ \csc(A)={c\over a} $$
$$ \sec(A)= {c\over b} $$
$$ \cot(A)={b\over a} $$
If h is unknown, but the angle v is given, the area can be expressed by:
$$ A_\triangle={b \times c \times \sin \angle A\over 2} $$
$$ h= \sin v \times c $$
Sine sentence
$$ {\sin A\over a}={\sin B\over b}={\sin C\over c} $$
$$ {a\over \sin A}={b\over \sin B}={c\over \sin C} $$
Cosine sentence
$$ a^2=b^2+c^2-2bc \times \cos A\\ b^2=a^2+c^2-2ac \times \cos B\\ c^2=a^2+b^2-2ab \times \cos C $$
Reference triangle for given variables.
Graphs of some trigonometric functions; Note that each of these functions is periodic. Thus, the sine and cosine functions repeat every 2π, and the tangent and cotangent functions repeat every π.
Graphs of some trigonometric functions
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