Patricia Crane

Answered

2021-12-24

How do you evaluate $\mathrm{sin}\left(\frac{\pi }{6}\right)$ ?

Answer & Explanation

Tiefdruckot

Expert

2021-12-25Added 46 answers

Explanation:
Start with an equilateral triangle of side 2. The interior angle at each vertex must be $\frac{\pi }{3}$ since 6 such angles make up a complete $2\pi$ circle.
Then bisect the triangle through a vertex and the middle of the opposite side, dividing it into two right angled triangles.
These will have sides of length 2,1 and $\sqrt{{2}^{2}-{1}^{2}}=\sqrt{3}$. The interior angles of each right angled triangle are and $\frac{\pi }{2}$ with the $\frac{\pi }{6}$ coming from the fact that we have bicested one of the $\frac{\pi }{3}$ angles.
Then:
$\mathrm{sin}\left(\frac{\pi }{6}\right)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{12}{}$

user_27qwe

Expert

2021-12-30Added 230 answers

The exact value of
The result can be shown in multiple forms
Exact Form:
Decimal Form:
0.5

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