Discover The Value Of Sin 𝜋/6 – Its Calculation In A Right-Angled Triangle

sin 𝜋/6

sin 𝜋/6 is equal to 1/2 or 0.5

sin 𝜋/6 is a trigonometric function that gives the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle whose angle at one vertex is 𝜋/6 radians.

To compute this value, we first recognize that 𝜋/6 radians is equivalent to 30 degrees in standard position. This means that the triangle with angle 𝜋/6 radians has one of its acute angles measuring 30 degrees.

Next, we draw that triangle and label the sides relative to that angle as follows:

“`
|
| /|
hyp | / | opp
|/__30|
adj
“`

where hypotenuse (hyp) is the longest side opposite the right angle, adjacent (adj) is the side next to the angle, and opposite (opp) is the side opposite the angle.

Now, using the definitions of sin, cos, and tan, we can write:

sin 30° = opp/hyp

Since this is the same as sin 𝜋/6, we have:

sin 𝜋/6 = opp/hyp = 1/2

Therefore, sin 𝜋/6 is equal to 1/2 or 0.5.

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