What does it mean when an angle is said to be complementary in trigonometry?

When an angle is described as complementary in trigonometry, it means that the two angles involved add up to 90 degrees. This concept is fundamental in trigonometry because it is often used when dealing with right triangles, where one angle is always 90 degrees, and the other two angles must therefore be complementary to maintain the total of 180 degrees in any triangle.

For example, if one angle measures 30 degrees, its complementary angle would measure 60 degrees, because 30 + 60 = 90. This relationship is particularly useful when applying trigonometric functions, as it allows for easier calculations involving sine, cosine, and tangent of acute angles.

Understanding the concept of complementary angles is essential, particularly in solving problems that involve right-angle triangles and their properties.