Determining the Value of sin(150°) Using Known Sine Ratios

sin(150°)

To determine the value of sin(150°), we will first express 150° in terms of angles whose sine values are known

To determine the value of sin(150°), we will first express 150° in terms of angles whose sine values are known.

We know that sin(180°) = 0. However, 150° is smaller than 180°, so we can express 150° as the difference between 180° and some angle x.

180° – x = 150°

Simplifying the equation:

x = 180° – 150°

x = 30°

Now that we have expressed 150° as the difference between 180° and 30°, we can utilize the property sin(180° – x) = sin(x) to find the value of sin(150°):

sin(150°) = sin(180° – 30°)

Using the property mentioned above:

sin(150°) = sin(30°)

The sine of 30° is a known value. In a right-angled triangle with one angle measuring 30°, the ratio of the length of the side opposite the angle to the length of the hypotenuse is 1/2. So, sin(30°) = 1/2.

Therefore, sin(150°) = sin(30°) = 1/2.

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