Calculating sin120° | Understanding Trigonometric Functions and Ratios

sin120°

The sine function (sin) is a trigonometric function that relates the ratio of the length of a side opposite to an angle in a right triangle to the length of the hypotenuse

The sine function (sin) is a trigonometric function that relates the ratio of the length of a side opposite to an angle in a right triangle to the length of the hypotenuse. In this case, we are given an angle of 120°.

To calculate sin120°, we start by drawing a right triangle and labeling the angles and sides. Since 120° is an angle in the second quadrant, the reference angle would be 180° – 120° = 60°.

In the right triangle, we can label the side opposite to the reference angle as “y” and the hypotenuse as “r” (radius). The side adjacent to the reference angle would be 180° – 90° = 90° – 60° = 30°.

Using the trigonometric relationship sine (sin), we can write:

sin(120°) = sin(180° – 60°) = sin(60°)

Now, we can use the ratios of the sides in a 30°-60°-90° triangle. In a 30°-60°-90° triangle, the ratio of the side opposite the 60° angle to the hypotenuse is √3/2.

Therefore, sin(120°) = sin(60°) = √3/2.

So, sin120° is equal to √3/2.

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