We have an answer to "How do you evaluate sin⁡(π6) ?"

High School
Geometry
Trigonometry
Trigonometric Functions

Patricia Crane

Answered question

2021-12-24

How do you evaluate

\sin (\frac{π}{6})

Answer & Explanation

Tiefdruckot

Beginner2021-12-25Added 46 answers

Explanation:
Start with an equilateral triangle of side 2. The interior angle at each vertex must be

\frac{π}{3}

since 6 such angles make up a complete

2 π

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

\frac{π}{3}, \frac{π}{6}

and

\frac{π}{2}

with the

\frac{π}{6}

coming from the fact that we have bicested one of the

\frac{π}{3}

angles.
Then:

\sin (\frac{π}{6}) = \frac{opposite}{hypotenuse} = \frac{12}{}

user_27qwe

Skilled2021-12-30Added 375 answers

The exact value of $\sin (\frac{π}{6}) is \frac{1}{2}$
The result can be shown in multiple forms
Exact Form: $\frac{1}{2}$
Decimal Form:
0.5

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