How this instrument works
Sine is one of the two ratios that defines every angle in a right triangle, and for a short list of angles its value is simple enough to hold in memory rather than compute fresh each time. This page checks exactly that: type in an angle, recall what its sine should be, enter that recollection as a guess, and the sheet reports the true value, sin(angle), alongside the gap between the two.
Two related pages on this site already cover sine. One lists the exact, non-decimal values at five special angles worth memorizing outright; another returns sine, cosine, and tangent together as rounded decimals for any angle at all. This page uses that same plain sin(angle) relationship, but turns it into a recall check rather than a lookup — the point isn't reading off a figure, it's testing whether what you already carry in your head matches the real one.
A difference of exactly zero is worth celebrating rather than expecting every time: it means the recalled figure matched the true sine bit for bit, realistic only at a handful of angles, such as 30° and 90°, where sine happens to land on a tidy number rather than an endless decimal.
- Enter an Angle — degrees by default, though radians and turns both work.
- Recall sin(angle) from memory before checking anything on the page.
- Type that recollection into Your guess for sin(angle).
- Read Correct sin(angle), the true value the sheet computes independently.
- Check Difference: negative means your guess ran low, positive means high, zero means an exact match.
Worked example — three angles, three memory checks
At 30°, sine is exactly 0.5 — one of a handful of angles where the value is a clean fraction rather than an endless decimal. Recalling 0.5 from memory matches it exactly, giving a difference of 0.5 − 0.5 = 0, a flawless recollection.
At 45°, sine works out to √2 ⁄ 2 ≈ 0.7071067811865476; recalling 0.7 comes close but not exact, a difference of 0.7 − 0.7071067811865476 ≈ −0.0071067811865476, undershooting by well under a hundredth. At 90°, sine reaches its own maximum, exactly 1; a recollection of 1 matches it precisely, landing on a difference of 0 once again.
Questions
What is sin(30°) exactly?
Exactly 0.5 — one of the handful of angles where sine resolves to a clean fraction rather than an unending decimal, which is why it's worth memorizing outright rather than recomputing each time it comes up.
How close was a recollection of 0.7 for sin(45°)?
Off by about 0.0071. The true value of sin(45°) is √2 ⁄ 2 ≈ 0.7071067811865476, so an entry of 0.7 undershoots by roughly seven-thousandths, close enough to reflect a solid memory of the special-angle values.
How is this different from the exact trig values page on this site?
That page lists exact, non-decimal sine and cosine values for five special angles side by side, meant as a reference sheet. This page takes a single angle, asks for a recalled guess at its sine first, and only then reveals the true value and the gap — a self-check rather than a lookup table.
How is this different from the sine-cosine-tangent calculator on this site?
That calculator returns all three ratios for any angle immediately, with no guess involved at all. This page isolates sine alone, asks for an estimate before showing anything, and reports how far that estimate sat from the real value — testing recall rather than simply computing a result.
Why does sin(90°) equal exactly 1?
Because 90° marks sine's own maximum: as an angle climbs toward a quarter turn, the corresponding right triangle's height grows to match its hypotenuse exactly, and their ratio caps out at 1 rather than climbing any further.
Does a nonzero difference mean the recollection was wrong?
Not necessarily wrong, just imprecise — a small nonzero difference, like the −0.0071 seen when recalling 0.7 for sin(45°), still reflects a solid grasp of the value. Only an entry far from the true figure points to a genuine gap in memorized angles.