To understand whether sin(30°) is equal to sin(150°), we can start by using the unit circle and understanding the properties of sine in different quadrants.
The sine function is defined as the ratio of the opposite side to the hypotenuse in a right triangle. It can also be visualized on the unit circle, where the sine of an angle is the y-coordinate of the point on the circle at that angle.
Now, let’s evaluate each angle:
- sin(30°): From our knowledge or the unit circle, we know that the sine of 30 degrees is:
- sin(30°) = 0.5
- sin(150°): For 150 degrees, which is in the second quadrant of the unit circle, we can use the sine angle identity:
- sin(150°) = sin(180° – 30°) = sin(30°)
- Thus, we have:
- sin(150°) = 0.5
Since both values are equal, we conclude that:
Conclusion
sin(30°) = sin(150°) = 0.5
Therefore, sin(30°) is indeed equal to sin(150°).