sin60º
The value of sin60º is equal to 0
The value of sin60º is equal to 0.86602540378 (rounded to 11 decimal places).
To understand how to calculate sin60º, we need to know some basic trigonometry concepts.
In a right triangle, the sine function is defined as the ratio of the length of the side opposite the given angle to the hypotenuse. In this case, 60º is an angle in a right triangle.
To find the value of sin60º, let’s consider an equilateral triangle. An equilateral triangle is a triangle with all three sides of equal length, and all three angles measuring 60º.
In an equilateral triangle, if we draw a perpendicular line from one vertex to the opposite side (creating a right angle), we will have two congruent right triangles. Each of these triangles has an angle measuring 60º.
Let’s assume that the length of each side is 1 unit in our equilateral triangle. By drawing the perpendicular line, we divide the equilateral triangle into two congruent right triangles.
In one of these right triangles, we have an angle measuring 60º and the opposite side is the height of the triangle. The hypotenuse of the right triangle is the length of one side of the equilateral triangle.
Using the Pythagorean theorem, we can calculate the height of the right triangle. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, it becomes:
1² = h² + (1/2)²
1 = h² + 1/4
h² = 1 – 1/4
h² = 3/4
h = sqrt(3/4) = sqrt(3)/2
From the definition of the sine function, sin60º = opposite/hypotenuse. In our triangle, the opposite side of the 60º angle is the height (sqrt(3)/2) and the hypotenuse is 1.
Therefore, sin60º = (sqrt(3)/2) / 1 = sqrt(3)/2 = 0.86602540378 (rounded to 11 decimal places).
So, the value of sin60º is 0.86602540378.
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