To find a trigonometric expression that is equal to sin(72°), we can utilize known trigonometric identities and relationships. One useful approach is to relate angles and their sine values based on the properties of a pentagon.
First, we can recall that sin(72°) can be represented using the sine of complementary angles. The related angle here is sin(90° - 72°), which equals cos(18°). Therefore, we have:
sin(72°) = cos(18°)
Furthermore, utilizing the sine double angle identity, we can express sin(72°) as:
sin(72°) = 2 * sin(36°) * cos(36°)
Thus, sin(72°) can be framed using either cos(18°) or the product of the sine and cosine of 36°. In summary, the equivalent expression for sin(72°) can be denoted as:
cos(18°)2 * sin(36°) * cos(36°)
This highlights the interconnectedness of trigonometric functions and how angles can represent equivalent expressions within these relations.