Understanding the Value of sin(180°) | Explained and Simplified

sin(180°)

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

The sine of an angle is a trigonometric function that relates the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. However, when we consider the angle of 180°, it does not correspond to a proper right triangle, as the angle is completely flat.

In trigonometry, the sine function oscillates between -1 and 1 for angles between 0° and 360°. Specifically, sine is positive in the first and second quadrants (from 0° to 180°) and negative in the third and fourth quadrants (from 180° to 360°). For example, sin(30°) = 0.5, sin(60°) = √3/2, sin(90°) = 1, and sin(120°) = √3/2.

Now, sin(180°) equals sin(180° – 0°) and using the properties of sine, we can simplify it further to sin(180°) = -sin(0°). The sine of 0° is 0, so substituting, we get sin(180°) = -0 = 0.

Therefore, the value of sin(180°) is zero.

More Answers: