To understand if sin 30 degrees equals sin 150 degrees, we first need to look at the values of these sine functions based on the unit circle and basic trigonometric ratios.
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the hypotenuse. For standard angles, we can easily find the sine values:
- sin 30°: The sine of 30 degrees is a well-known value. It equals 0.5.
- sin 150°: To find sin 150 degrees, we can use the sine function’s property that states sin(180° – x) = sin x. Therefore, sin 150° = sin(180° – 30°) = sin 30°. Since we already know that sin 30° = 0.5, we conclude that sin 150° also equals 0.5.
Thus, we can confidently say that sin 30° is equal to sin 150°, as both values are 0.5. This is a result of the symmetry of the sine function in the unit circle.