The Pythagorean identity, sin²θ + cos²θ = 1, ties the two main ratios of an angle together: know one and the other is fixed. These free printable worksheets give one ratio of an acute angle and ask for the other, exact as a fraction.
Kid stuck on one? You don’t just get the sheet.
The answer key prints on a separate page.
Every question is built off a Pythagorean triple, so knowing sin A = 3/5 gives cos A = 4/5 exactly — a clean fraction, not a decimal. The work is recognising the triple and reading off the side that is left, which is the identity doing what Pythagoras does on the triangle behind it.
It needs no calculator, so the page prints and the answers stay exact. The step-by-step walk states the identity first and then applies it, because the point is seeing that one ratio determines the other rather than grinding an arithmetic routine.
One question from this sheet, worked through a step at a time.
Find sin A
