The diameter of a circle.

Trigonometry equalities, inequalities and expressions - sin, cos, tan, cot

The diameter of a circle.

Postby Guest » Wed Nov 28, 2018 8:05 pm

The inverse of one angle and the side opposite to the angle, which is equal to one, in all triangles gives a diameter of the circumscribed circle.

In a right triangle the inverse of the angle is always 1 which is the circle's diameter, and its' opposite's side is 1, that is hypotenuse of 1. $\sin 90 =1$ is the angle $\theta$.



My question is, what is the right explanation concerning the inverse of angles with sides $a,b,c$ for all $\triangle ABC$ when the base or the hypotenuse equals to 1?

1)explanation

I have three sides $5, 5, 4$ and $1.25, 1.25, 1$ with all the same angles except the base is 1, and all I did is divide sides $5, 5, 4$ by 4 to obtain the the simplyfied version of the triangle sides. $1.25, 1.25, 1$ . From the $\triangle ABC $ and 1 the side $c$ opposite to the $\angle C =\sqrt (1-0.68^2)$. Its' inverse is the diameter of circumscribed circle in term of $\sin$ but not in terms of Cosine.

The law of Sine states that :

$$\frac {\sin A}{a}=\frac {\sin B}{b}=\frac {\sin C}{c}=\frac {1}{d}$$ where d is the diameter.

$$\frac {a}{\sin A}=\frac {b}{\sin B}=\frac {c}{\sin C}={d}$$ where d is the diameter.
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