The special angles — 0, 30, 45, 60 and 90 degrees — have exact values a student is meant to know by heart. These free printable worksheets ask for sin, cos and tan at each, left exact as a surd or a fraction rather than a decimal.
Kid stuck on one? You don’t just get the sheet.
The answer key prints on a separate page.
The values come straight off two triangles: the 30-60-90 with sides 1, √3, 2, and the 45-45-90 with sides 1, 1, √2. So sin 30° is 1/2, cos 45° is √2/2, tan 60° is √3 — read off the sides, never rounded. A calculator's 0.866 hides the √3/2 the student is supposed to recognise, which is why this page prints and keeps the answer exact.
The answers are stacked the way a book writes a fraction, and the step-by-step walk names the triangle each value comes from. Learning them is what makes the unit circle and later identities quick rather than a lookup every time.
One question from this sheet, worked through a step at a time.
Find tan 60°
