Complementary angles and cofunctions

Complementary angles and cofunctions

Explain why trigonometric functions pair naturally when two acute angles add to a right angle. This precalculus practice set develops the sine–cosine, tangent–cotangent and secant–cosecant relationships from the opposite and adjacent sides of one right triangle.

Use a labelled diagram to track how side roles change, rewrite a function using its cofunction, transfer known values, and combine complementary-angle reasoning with reciprocal ratios. Multiselect questions require checking all proposed equalities. Restricted angle problems include simple algebra, while a radian example reinforces that the complement depends on the angle unit being used.

Prerequisites and approach

Review the six right-triangle ratios, special-triangle values and degree–radian conversion. Sketch the two acute angles and label their shared hypotenuse before manipulating symbols. The explanations distinguish a cofunction at the complementary angle from a reciprocal at the same angle. Every equation-solving task explicitly restricts its relevant angles to be acute; solving general trigonometric equations over arbitrary intervals is reserved for later modules. Worked counterexamples help test whether a proposed relationship holds for all acute angles.