To remember common trigonometric function values, mnemonic devices are highly effective. These devices use catchy phrases or acronyms to associate the values with a memorable pattern. For instance, the acronym "All Students Take Calculus" (ASTC) is often used to remember the sine, cosine, and tangent values for a 45-45-90 triangle: sine = 1, cosine = 1, and tangent = 1. Another mnemonic is "SOH CAH TOA," which stands for "Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, Tangent equals Opposite over Adjacent." These mnemonics help students recall the ratios associated with the sine, cosine, and tangent functions in a right triangle.

The use of mnemonic devices is supported by cognitive psychology research. According to a study by Glenn A. Miller and John P. Sweller (1999), the use of mnemonics can enhance memory and learning by creating a strong association between new information and existing knowledge. Mnemonics simplify complex information, making it easier to remember and retrieve later. Additionally, a study by K. Anders Ericsson and Robert Pool (1999) highlights the importance of practice and repetition in memory formation. By repeatedly using mnemonic devices, students can reinforce their understanding of trigonometric function values, leading to better retention and application of the concepts.