How do you evaluate sin⁡(π6) ?

Patricia Crane

Patricia Crane

Answered

2021-12-24

How do you evaluate sin(π6) ?

Answer & Explanation

Tiefdruckot

Tiefdruckot

Expert

2021-12-25Added 46 answers

Explanation:
Start with an equilateral triangle of side 2. The interior angle at each vertex must be π3 since 6 such angles make up a complete 2π 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 2212=3. The interior angles of each right angled triangle are π3, π6 and π2 with the π6 coming from the fact that we have bicested one of the π3 angles.
Then:
sin(π6)=oppositehypotenuse=12
user_27qwe

user_27qwe

Expert

2021-12-30Added 230 answers

The exact value of sin(π6) is 12
The result can be shown in multiple forms
Exact Form: 12
Decimal Form:
0.5

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